Perpendicular Velocity Component Research Articles

Colloid Particle Adsorption in the Slot Impinging Jet Cell

A detailed description of flow distribution in the slot impinging jet cell (SIJ) is presented. Numerical solutions of the governing Navier–Stokes equation showed that forRe< 30 the flow resembles closely the one occurring near a cylinder placed in a uniform flow. It was also shown that for tangential distancesx/d< 0.25 the flow configuration in the vicinity of the solid can be approximated by the plane-parallel stagnation flow with the perpendicular velocity component independent of this distance. This flow field was used for deriving the mass transfer equation, which was then numerically solved to obtain the initial flux (adsorption rate) for various transport conditions. These theoretical predictions were verified experimentally using polystyrene latex particles of the size 1 and 1.48 μm. A good agreement between predicted and measured initial flux values was found for a broad range of Reynolds number and ionic strength of the particle suspension. This confirmed that the SIJ cell surface was uniformly accessible for particles at distancesx/d< 0.5. At larger distances a systematic deviation from uniform deposition rates was observed, becoming important for higher coverages andRe.This effect was attributed to the hydrodynamic scattering of adsorbing particles on particles already attached to the surface. This phenomenon was quantitatively accounted for by the Brownian dynamics type simulations.

Closure of multi-fluid and kinetic equations for cyclotron-resonant interactions of solar wind ions with Alfvén waves

Abstract. Based on quasilinear theory, a closure scheme for anisotropic multi-component fluid equations is developed for the wave-particle interactions of ions with electromagnetic Alfvén and ion-cyclotron waves propagating along the mean magnetic field. Acceleration and heating rates are calculated. They may be used in the multi-fluid momentum and energy equations as anomalous transport terms. The corresponding evolution equation for the average wave spectrum is established, and the effective growth/damping rate for the spectrum is calculated. Given a simple power-law spectrum, an anomalous collision frequency can be derived which depends on the slope and average intensity of the spectrum, and on the gyrofrequency and the differential motion (with respect to the wave frame) of the actual ion species considered. The wave-particle interaction terms attain simple forms resembling the ones for collisional friction and temperature anisotropy relaxation (due to pitch angle scattering) with collision rates that are proportional to the gyrofrequency but diminished substantially by the relative wave energy or the fluctuation level with respect the background field. In addition, a set of quasilinear diffusion equations is derived for the reduced (with respect to the perpendicular velocity component) velocity distribution functions (VDFs), as they occur in the wave dispersion equation and the related dielectric function for parallel propagation. These reduced VDFs allow one to describe adequately the most prominent observed features, such as an ion beam and temperature anisotropy, in association with the resonant interactions of the particles with the waves on a kinetic level, yet have the advantage of being only dependent upon the parallel velocity component.

Development of a novel ion energy analyser to measure the energy distribution function f( v∩, v|) of end-loss ions from FRC plasmas

A novel ion energy analyser is developed to measure the energy distribution function f( v∩, v|) of ions lost from both ends of FRC (field-reversed configuration) plasmas. Simultaneous measurement of both parallel and perpendicular velocity components is carried out in a straight and static magnetic field. The parallel velocity component of the end-loss ions is analysed by a retarding potential parallel to the magnetic field. Selection of perpendicular energy is made by the difference in particular gyroradius in a given magnetic field. A trial to confirm the applicability has been performed on the end: loss flow from the field-reversed configuration plasma produced by the FIX (FRC injection experiment) machine.

Dilatant double shearing theory applied to granular chute flow

Although the steady flow of a granular material down a plane inclined slope has been exhaustively examined from both theoretical and experimental points of view, there is still no general agreement concerning the basic flow properties such as density and velocity profiles. The majority of studies assume that the velocity component of the material perpendicular to the inclined plane is sufficiently small to assume that it is everywhere zero. However, recent dynamical modelling of granular chute flow indicates that this component of velocity, although small, is actually non-zero. In this paper, we examine a dilatant double shearing theory for chute flow assuming that the perpendicular component of velocity is non-zero. An explicit analytical form for the perpendicular velocity profile is deduced which gives rise to an integral expression for the chute stream velocity. Assuming a linear decreasing density profile, numerical integration for the chute stream velocity predicts a non-linear profile which is concave in shape and which is in agreement with recent results from computer simulation and existing experimental data in the literature.

On the pulsar radiation mechanism

Pulsars have typical magnetic field strengths between 108and 1012G. Therefore, even if the particles are produced with nonzero perpendicular component of velocity at the pole, they radiate out this component quickly due to synchrotron radiation. Therefore, the motion of a particle along a field line becomes one dimensional in regions where filed lines are straight. However, when they move along the curved magnetic field lines, they get accelerated due to the centrifugal force. They gain again the perpendicular energy at the expense of parallel energy, but can not gyrate in the curved field lines and hence do not experience any curvature or gradient drifts.

Do hollow atoms exist in front of an insulating LiF(100) surface?

First measurements of KLL Auger spectra arising from collisions of N6+ ions on an insulating LiF(100) surface are presented. The beam energy is varied from 0.08 up to 16 keV. The incident angle is chosen such that the perpendicular velocity component is constant over the indicated energy range. Spectral features arising from above surface KLL emission, observed during interaction of N6+ with a conducting Si(100) surface, are absent for LiF, implying pronounced differences in the dynamics governing the above-surface neutralization and deexcitation of the highly charged projectiles.

The electron foreshock

An overview of the observations of backstreaming electrons in the foreshock and the mechanisms that have been proposed to explain their properties will be presented. A primary characteristic of observed foreshock electrons is that their velocity distributions are spatially structured in a systematic way depending on distance from the magnetic field line which is tangent to the shock. There are two interrelated aspects to explaining the structure of velocity distributions in the foreshock, one involving the acceleration mechanism and the other, propagation from the source to the observing point. First, the source distribution of electrons energized by the shock must be determined along the shock surface. Proposed acceleration mechanisms include magnetic mirroring of incoming solar wind particles and mechanisms involving transmission of particles through the shock. Secondly, the kinematics of observable electrons streaming away from a curved shock with an initial parallel velocity and a downstream perpendicular velocity component due to the motional electric field must be determined. This is the context in which the observations and their explanations will be reviewed.

Heat transport in PBX-M high beta p plasmas

High poloidal beta discharges in PBX-M routinely enter the H mode regime: typically, a quiescent phase followed by an MHD-active phase characterize the H mode period. An analysis of the energy transport during these phases is conducted using the experimental data and the code TRANSP; effective thermal diffusivities are computed. The quiescent H phase is characterized by a decrease of the thermal ion energy transport and a flattening of the associated effective diffusivity profile. Enhanced fast ion losses are observed during the MHD-active phase; particles in the lower end of the fast-ion energy spectrum with a large perpendicular velocity component are predominantly affected. Folding these losses into the analysis permits to reproduce the measured stored energy and time evolution of the neutron production rate during the MHD-active phase. During the MHD-active phase, the ion thermal diffusivity maintained a profile (magnitude and shape) similar to that obtained at the end of the quiescent H phase, suggesting, within the uncertainty of this analysis, that the MHD activity does not affect the thermal plasma energy transport. The observed stored energy (beta) saturation results from the enhanced losses in the fast-ion population. An analysis without inclusion of enhanced fast ion losses fails to reproduce the experimental measurements. Throughout the H mode period the electron effective diffusivity remains lower than the ion effective diffusivity. An error analysis is presented

F region plasma drifts over Arecibo: Solar cycle, seasonal, and magnetic activity effects

We have used Arecibo incoherent scatter measurements from 1981 to 1990 to determine the characteristics of low‐latitude F region plasma drifts. The measurements show large day‐to‐day variability even during magnetically quiet periods. The average poleward/perpendicular plasma drifts do not change significantly with season and solar cycle except in the midnight‐morning sector. The zonal drifts show clear solar cycle and seasonal effects. The afternoon‐nighttime eastward drifts increase with solar flux; the westward drifts in the early morning‐afternoon sector show a large increase from summer to winter but are independent of solar activity. The two perpendicular velocity components also respond differently to magnetic activity. The average northward/perpendicular drifts decrease with magnetic activity during the day but do not exhibit a systematic response at night. The zonal component shows increased westward drifts occurring predominantly at night. The plasma drifts along the magnetic field lines exhibit large altitudinal and seasonal variations, particularly near solar minimum, and are generally anticorrelated with the perpendicular/north drifts. The drift patterns observed by the Arecibo and the middle and upper atmosphere radars have significantly different seasonal dependence. This can be explained by electrodynamic effects in the corresponding local and conjugate ionospheres. The large longitudinal variation of the quiet time F region plasma drifts results from the displacement between the geographic and dip equators and from magnetic field declination effects. In general, the longitudinal variation should also depend on magnetic activity.

Collisional equipartition rate for a magnetized pure electron plasma

The collisional equipartition rate between the parallel and perpendicular velocity components is calculated for a weakly correlated electron plasma that is immersed in a uniform magnetic field. Here, parallel and perpendicular refer to the direction of the magnetic field. The rate depends on the parameter κ̄=(b̄/rc)/, where rc=(T/m)1/2/Ωc is the cyclotron radius and b̄=2e2/T is twice the distance of closest approach. For a strongly magnetized plasma (i.e., κ̄≫1), the equipartition rate is exponentially small (ν∼exp[−5(3πκ̄)2/5/6]). For a weakly magnetized plasma (i.e., κ̄≪1), the rate is the same as for an unmagnetized plasma except that rc/b̄ replaces λD/b̄ in the Coulomb logarithm. (It is assumed here that rc&amp;lt;λD; for rc&amp;gt;λD, the plasma is effectively unmagnetized.) This paper contains a numerical treatment that spans the intermediate regime κ̄∼1, and connects onto asymptotic results in the two limits κ̄≪1 and κ̄≫1. Also, an improved asymptotic expression for the rate in the high-field limit is derived. The present theoretical results are in good agreement with recent measurements of the equipartition rate over eight decades in κ̄ and four decades in the scaled rate ν/nv̄b̄2, where n is the electron density and v̄=(2T/m)1/2.

Analysis and design of an anamorphic optical processor for speckle metrology and velocimetry

Two-dimensional velocity or displacement fields that are recorded as double-exposure speckle patterns may be measured with an anamorphic optical processor. The anamorphic optical processor measures one component of the velocity or displacement throughout a linear region of the double-exposure speckle pattern. The signal in the output plane of such a processor is a fringe pattern. An analysis to predict fringe modulation based on Fourier optics and the statistics of speckle patterns is developed. The analysis specifies the effects of both the speckle-recording optics and the anamorphic optical processor on the fringe modulation. The observed loss of modulation when the velocity or displacement component perpendicular to the measured component is increased is also described. Measurements of fringe modulations that are produced by anamorphic optical processors with and without increased tolerance to the perpendicular velocity component are compared to results of the analysis. Fringe modulation versus relative exposure in the double-exposure speckle pattern are also measured and compared to the results of this analysis. An anamorphic processor that reduces the time for digital processing of the fringe patterns by a factor of N (typically 128, 256, or 512) relative to the two-dimensional Fourier transform optical processor (with identical spatial resolution) is demonstrated.

Stimulated emission of AKR in regions of a weakly unstable electron velocity distribution

It is generally believed that auroral kilometric radiation (AKR) originates in regions in which energetic auroral electrons possess a velocity distribution with a loss‐cone feature. According to the cyclotron maser theory of AKR, the resulting instability can be substantial in some regions of the auroral zone, leading to the generation of radiation with many features that are consistent with the observations. However, in situ measurements of velocity distributions obtained with satellites only show evidence of moderate positive gradients in the perpendicular velocity component υ⊥. Such distributions prove to be only marginally unstable, and thus imply a low level of radiation. From this point of view it is of interest to study the amplification of externally generated radiation. This radiation might originate from adjacent regions with a more unstable velocity distribution or from remote sources in space. In this work we perform numerical simulation studies using alternatively an observed electron velocity distribution, obtained from DE 1 measurements, and an idealized loss‐cone distribution. The results show the expected amplification of X mode radiation as well as effects which go beyond the behavior of a simple amplifying medium. Whereas wave growth is exponential for the idealized loss‐cone distribution, it is initially linear in time in the weakly unstable case, following the increase of the external wave power in the simulation. At later stages the collective properties of the plasma lead to interesting effects, such as the continuation of wave growth after cessation of the external wave in cases which do not exhibit growth otherwise, and a threshold power level before growth occurs. We suggest that these phenomena are relevant to the understanding of the observed enhancement and triggering of AKR due to solar radio bursts.

Velocity field computation using neural networks

A new approach for optical flow (image velocity) fields computation is presented using computational neural networks. The computational procedure consists of three stages: estimation of the parameters of the neural network model, dynamic measurement of the perpendicular velocity components of the contours or region boundaries and computation of the image velocity fields. The parameters are estimated by comparing the energy function of the neural network with a constrained error function. The nonlinear velocity fields computation method is then carried out iteratively by using a dynamic algorithm to minimise the energy function simultaneously with the dynamic measurement of the perpendicular velocity components by a dynamic procedure. Experiments generate velocity fields that are meaningful and consistent with visual perception.

Dynamic estimation of optical flow field using objective functions

Optical flow (image velocity) fields are computed and interpreted from an image sequence by incorporating knowledge of object kinematics. Linear and quadratic objective functions are defined by considering the kinematics, and the function parameters are estimated simultaneously with the computation of the velocity field by relaxation. The objective functions provide an interpretation of the dynamic scenes and, at the same time, serve as the smoothness constraints. The computation is initially based on measured perpendicular velocity components of contours or region boundaries which, due to the ‘aperture problem’, are theoretically not the true perpendicular velocity components. This difficulty is alleviated by introducing a dynamic procedure for the measurement of the perpendicular components. Experiments on using objective functions for synthetic and real images of translating and rotating objects generated velocity fields that are meaningful and consistent with visual perception.

Plasma drifts associated with a system of Sun‐aligned arcs in the polar cap

A series of four sun‐aligned arcs passed over Sondre Stromfjord, Greenland, on the night of the 17th and 18th of February, 1985. Observations of these arcs were made using the Sondrestrom incoherent scatter radar and an intensified all‐sky imaging TV system that was operated at the radar site. The first of the four arcs crossed the Sondre Stromfjord meridian just before local midnight moving westward, and the other three arcs followed at approximately half‐hour intervals. When we account for the earth's rotation, the arc drift in an inertial frame was eastward, or dusk to dawn. The half‐hour interval between meridian crossings of the arcs implies that the mean spacing between the arcs was 180 km. A Defense Meteorological Satellite Program (DMSP) F6 satellite pass at 0110 UT revealed the presence of highly structured electron and ion precipitation throughout the polar cap. The DMSP visible imager detected a single, sun‐aligned arc associated with the largest peak in precipitating electron flux. This arc was also observed at Thule, Greenland, with an intensified film camera. These observations suggest that at least one of the arcs that were observed at Sondre Stromfjord extended across a large part of the polar cap. The radar at Sondre Stromfjord measured electron density and ion drift velocities associated with the four arcs. The radar drift measurements were superimposed on the all‐sky video images to determine the location of the measurements relative to the arcs. Plasma drifts outside the arcs were found to be both sunward and antisunward, while within the arcs the drifts were predominantly antisunward. The variability of the drifts in the direction parallel to the arcs indicates that the electric fields were highly structured even though the configuration and motion of the arcs were well behaved. The motion of the auroral forms perpendicular to the arcs was generally in the same direction as the perpendicular component of the plasma velocity.

Two-component velocity measurements in a supersonic nitrogen jet with spatially resolved inverse Raman spectroscopy

Using inverse Raman spectroscopy (IRS), we directly measured two perpendicular velocity components by crossing two probe laser beams symmetrically with the pump laser beam. Because of the crossing, the spatial resolution was improved by more than 1 order of magnitude compared with that obtained with previous IRS measurements. This made it possible to map out the planar velocity and temperature distributions in a supersonic N(2) jet. The measured distributions are in good agreement with theoretical calculations. Extension to the measurement of all three velocity components is discussed.

Velocity dependence of secondary-ion emission

The emission probability ${S}^{+}(v)$ of secondary ions ejected along the surface normal from polycrystalline Cr, Ag, Cu, and Zr is found to be strongly dependent upon the velocity of the secondary ion. The dependence of ${S}^{+}(v)$ on the perpendicular velocity component is in qualitative agreement with theories in which the ion formation is governed by a time-dependent perturbation of the outer electronic structure of the atom as it crosses the boundary of the surface into the vacuum. Plots of ${log}_{10}{S}^{+}(v)$ against ${v}^{\ensuremath{-}1}$ show linearity in the energy region $4\ensuremath{\le}E\ensuremath{\le}30$ eV, with slopes of the order of (2-3)\ifmmode\times\else\texttimes\fi{}${10}^{6}$ cm/sec. Thus exponential dependence of ${S}^{+}(v)$ predicted by the time-dependent perturbation theories is observed, at least over a limited energy range. A simple image-force correction extends adherence to linearity below 4 eV, with ion yields as low as ${10}^{\ensuremath{-}6}$. Positive deviation from the linear dependence of ${S}^{+}(v)$ is observed in each case for secondary ions with $E&gt;30$ eV. This energy region may also be fitted with an exponential dependence of ${S}^{+}(v)$, yielding slopes within the range of (3-6)\ifmmode\times\else\texttimes\fi{}${10}^{6}$ cm/sec.

The velocity dependence of secondary ion fields

The yield of secondary ions ejected along the surface normal from polycrystalline Cr, Ag, Cu and Zr is only found to be strongly dependent upon the velocity of the ion. The dependence of the ion yields, S +( v), in the perpendicular velocity component, is in qualitative agreement with theories in which is ion formation is governed by a time-dependent perturbation of the outer electronic structure of the atom as it crosses the boundary of the surface into the vacuum. Plots of log S +( v) against v − show linearity in the energy region 4⩽ E⩽30 eV, with slopes of the order of 2–3×10 6 cm/s. Thus, exponential dependence of S +( v) predicted by the time-dependent perturbation theories is observed, at least over a limited energy range. A simple image force correction extends adherence to linearity below 4 eV, with ion yields as low as 10 −6. Positive deviation from the linear dependence of S +( v) is observed in each case for secondary ions with E >30 eV. This energy region may also fit with an exponential dependence of S +( v), yielding slopes within the range of 3 to 6×10 6 cm/s.

A two-dimensional velocity analyser for electrons produced in laboratory plasma experiments

A two-dimensional velocity analyser is described, for use in laboratory plasmas with an axial magnetic field. An applied electric field, perpendicular to the magnetic field, preferentially selects electrons depending on their initial parallel (axial) velocity component. Subsequent sampling of the selected electrons with a retarding potential analyser, in a region of reduced magnetic field, enables the authors to determine both perpendicular and parallel velocity components of the electrons. The characteristics of the instrument are discussed and measurements made with the prototype instrument are compared with the results from a computer simulation. Some applications of this instrument as a diagnostic tool for use with laboratory plasmas are given.

Correlation of wind and electric field in the nocturnal F-region

Summary. The incoherent scatter radar at the Arecibo Observatory measures the ion drift velocity vector in the E- and F-regions of the ionosphere. This vector can be resolved into components parallel and perpendicular to the geomagnetic field. Nocturnal F-region data reveal a particularly marked negative correlation between the parallel component, which represents the combined effects of diffusion and a meridional wind, and the perpendicular component, which is caused by a zonal electric field. Various explanations of this correlation have been offered. One is that ion drag causes the F-region wind to respond to changes in the ion drift velocity. This explanation is not adequate, however, because nocturnal ion densities are too low for ion drag to affect the wind on the observed time scales of an hour or less. Another mechanism suggests that F-region winds lead to the generation of F-region polarization electrostatic fields, causing the perpendicular drift to respond to changes in the wind. Analysis of the data suggests that this mechanism does not account for the most striking examples of the correlation (those with short period), although it may operate weakly. The mechanism that appears to be most successful in accounting for the phenomenon attributes changes in the parallel component of the ion drift velocity to changes in the diffusion velocity resulting from changes in the F-layer height which result, in turn, from changes in the zonal electric field. Why the electrostatic field in the nocturnal ionosphere (and thus the perpendicular component of the ion drift velocity) should fluctuate as widely as the Arecibo data reveal is not known.