Bimodal Velocity Distribution Research Articles

Inflow and shock formation in supersonic, rarefied plasma expansions

In this paper the physics of plasma expansion in the rarefied regime is reviewed. Densities, temperatures, and velocity distributions in argon, hydrogen, and nitrogen expansions that have been measured using laser scattering and fluorescence techniques are compared. The velocity distributions in the region of the expansion where the density is below the background density show a bimodal character. It is interpreted in terms of a component expanding from the source and a component flowing into the plasma expansion from the periphery. Also in the shock of the expansion, bimodal velocity distributions are encountered. These distributions show the gradual change in the flow from supersonic to subsonic—the formation of the shock. From a comparison of the three expansions, a general view of the shock formation is derived. This new insight leads to a better understanding of how the chemical reactivity of the usually impenetrable, supersonic plasma can be used most efficiently.

The origin of the rotational and spatial velocities of radio pulsars

We analyze possible origins of the observed high rotational and spatial velocities of radio pulsars. In particular, these can be understood if all radio pulsars originate in close binary systems with orbital periods of 0.1–100 days, with the neutron star being formed by a type Ib,c supernova. The high spatial velocities of pulsars (v p up to 1000 km/s) reflect the high Keplerian velocities of the components of these binaries, while their short periods of rotation (P p < 4 s) are due to the rapid rotation of the presupernova helium-star components with masses of 2.5–10 M ⊙, which is synchronous with their orbital rotation. Single massive stars or components in wide binaries are likely to produce only slowly rotating (P p > 4 s) neutron stars or black holes, which cannot be radio pulsars. As a result, the rate of formation of radio pulsars should be a factor of a few lower than the rate of type II and type Ib,c supernovae estimated from observations. This scenario for the formation of radio pulsars is supported by (i) the bimodal spatial velocity distribution of radio pulsars; (ii) the coincidence of the observed spatial velocities of radio pulsars with the orbital velocities of the components of close binaries with nondegenerate helium presupernovae; (iii) the correlation between the orbital and rotational periods for 22 observed radio pulsars in binaries with elliptical orbits; and (iv) the similarity of the observed rate of formation of radio pulsars and the rate of type Ib,c supernovae.

Pulsar Kicks via Spin-1 Color Superconductivity

We propose a new neutrino propulsion mechanism for neutron stars which can lead to strong velocity kicks, needed to explain the observed bimodal velocity distribution of pulsars. The spatial asymmetry in the neutrino emission is naturally provided by a stellar core containing spin-1 color-superconducting quark matter in the A phase. The neutrino propulsion mechanism switches on when the stellar core temperature drops below the transition temperature of this phase.

A statistical study of 233 pulsar proper motions

We present and analyse a catalogue of 233 pulsars with proper motion measurements. The sample contains a wide variety of pulsars including recycled objects and those associated with globular clusters or supernova remnants. After taking the most precise proper motions for those pulsars for which multiple measurements are available, the majority of the proper motions (58%) are derived from pulsar timing methods, 41% using interferometers and the remaining 1% using optical telescopes. Many of the 1-D and 2-D speeds (referring to speeds measured in one coordinate only and the magnitudes of the transverse velocities respectively) derived from these measurements are somewhat lower than earlier estimates because of the use of the most recent electron density model in determining pulsar distances. The mean 1-D speeds for the normal and recycled pulsars are 152(10) and 54(6) km/s respectively. The corresponding mean 2-D speeds are 246(22) and 87(13) km/s. PSRs B2011+38 and B2224+64 have the highest inferred 2-D speeds of ~1600 km/s. We study the mean speeds for different subsamples and find that, in general, they agree with previous results. Applying a novel deconvolution technique to the sample of 73 pulsars with characteristic ages less than 3 Myr, we find the mean 3-D pulsar birth velocity to be 400(40) km/s. The distribution of velocities is well described by a Maxwellian distribution with 1-D rms sigma=265 km/s. There is no evidence for a bimodal velocity distribution. The proper motions for PSRs B1830-08 and B2334+61 are consistent with their proposed associations with the supernova remnants W41 and G114.3+0.3 respectively.

Random Heterogeneous Model with Bimodal Velocity Distribution for Methane Hydrate Exploration

We have developed a random heterogeneous velocity model with bimodal distribution in methane hydrate-bearing zones. The P-wave well-log data have a von Karman type autocorrelation function and non-Gaussian distribution. The velocity histogram has two peaks separated by several hundred metres per second. A random heterogeneous medium with bimodal distribution is generated by mapping of a medium with a Gaussian probability distribution, yielded by the normal spectral-based generation method. By using an ellipsoidal autocorrelation function, the random medium also incorporates anisotropy of autocorrelation lengths. A simulated P-wave velocity log reproduces well the features of the field data.This model is applied to two simulations of elastic wave propagation. Synthetic reflection sections with source signals in two different frequency bands imply that the velocity fluctuation of the random model with bimodal distribution causes the frequency dependence of the Bottom Simulating Reflector (BSR) by affecting wave field scattering. A synthetic cross-well section suggests that the strong attenuation observed in field data might be caused by the extrinsic attenuation in scattering.We conclude that random heterogeneity with bimodal distribution is a key issue in modelling hydrate-bearing zones, and that it can explain the frequency dependence and scattering observed in seismic sections in such areas.

Bimodal velocity distribution of atoms released from nanosecond ultraviolet laser ablation

We have investigated the velocity distributions of atoms released from a metallic gadolinium surface by UV laser ablation. The fluences of the nanosecond laser pulses were chosen for a pure release of neutrals and at a higher fluence level for the release of both neutrals and ions. In both cases a thermal Maxwell-Boltzmann slope has been observed for the low velocities, whereas for high velocities strong deviations from a thermal distribution have been seen. The observed velocity distribution has been explained by a bimodal structure including a thermal phase and a shockwave driven ``blow-off'' phase.

Random heterogeneous model with bimodal velocity distribution for Methane Hydrate exploration

We have developed a random heterogeneous velocity model with bimodal distribution in methane hydrate-bearing zones. The P-wave well-log data have a von Karman type autocorrelation function and non-Gaussian distribution. The velocity histogram has two peaks separated by several hundred metres per second. A random heterogeneous medium with bimodal distribution is generated by mapping of a medium with a Gaussian probability distribution, yielded by the normal spectral-based generation method. By using an ellipsoidal autocorrelation function, the random medium also incorporates anisotropy of autocorrelation lengths. A simulated P-wave velocity log reproduces well the features of the field data.This model is applied to two simulations of elastic wave propagation. Synthetic reflection sections with source signals in two different frequency bands imply that the velocity fluctuation of the random model with bimodal distribution causes the frequency dependence of the Bottom Simulating Reflector (BSR) by affecting wave field scattering. A synthetic cross-well section suggests that the strong attenuation observed in field data might be caused by the extrinsic attenuation in scattering.We conclude that random heterogeneity with bimodal distribution is a key issue in modelling hydrate-bearing zones, and that it can explain the frequency dependence and scattering observed in seismic sections in such areas.

Evaporation of high speed sporadic meteors

Abstract. Recent measurements conducted at the Arecibo Observatory report high-speed sporadic meteors having velocities near 50 km/s. The results seem to indicate a bimodal velocity distribution in the sporadic meteors (maxima at ~20 km/s and ~50 km/s). The particles have a maximum mass of ~1µg. This paper will present an analysis of the ablation of 1µg meteoroids having velocities of 20, 30, 50, and 70 km/s. The calculations show that there is fractionation even for the fast meteoroids, the effect being particularly noticeable for the 1µg sporadic particles, and less so for the heavier particles. The relevance of the calculations to the radar observations of the sporadic meteors will be discussed.

Suspension and fall of heavy particles in random two-dimensional flow.

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.

Compressibility effects on turbulence structures of axisymmetric mixing layers

A real-time flow visualization system that produces 17 images over a time span of 150 μs is used to visualize the mixing layers of Mach 1.3 (Mc=0.59) and Mach 2.0 (Mc=0.87) ideally expanded high Reynolds number axisymmetric jets. These image sequences reveal details about the influence of compressibility on the dynamics of turbulence structures. In general, the behavior observed in axisymmetric jets is similar to that observed in planar shear layers at similar convective Mach numbers. In addition, large streamwise vortices are apparent in cross-stream images of the flow. Large-scale structures become more three-dimensional and less organized with increasing compressibility and more difficult to identify and track. Planar space–time correlations are used to track structures as they convect downstream. The histogram of the convective velocity for the Mach 1.3 jet revealed a broad distribution of convective velocities with an ensemble average of 266 m/s, which is much higher than the theoretical prediction of 206 m/s. The Mach 2.0 jet, however, exhibited a bimodal convective velocity distribution with an ensemble average of 402 m/s for the “fast” and 190 m/s for the “slow” mode. These modes are equally spaced from the theoretical convective velocity of 303 m/s. Approximately 2/3 of the measured velocities were in the slow mode.

Ion-imaging of the photodissociation of CF3I+

The photodissociation of CF3I+ prepared by resonance enhanced multiphoton ionization has been studied by using velocity-map ion imaging and photoelectron spectroscopy. Photodissociation of CF3I+ between 300 and 306 nm results in dissociation to both CF3+I+ and CF3++I. As in an earlier study using time-of-flight mass spectrometry [L. D. Waits et al., J. Chem. Phys. 97, 7263 (1992)], the latter channel displays a bimodal velocity distribution, indicative of two different dissociation mechanisms. Photoelectron spectra presented here indicate that, contrary to the earlier suggestion, these dissociation processes must both occur following excitation to the A 2A1 state or to another dissociative state of the ion, and the ion images are consistent with this conclusion. The photoelectron angular distributions extracted from the ion images also provide new perspective on earlier studies of the dissociative ionization of CF3I.

On-off intermittency and intermingledlike basins in a granular medium.

Molecular dynamic simulations of a medium consisting of disks in a periodically tilted box yield two dynamic modes differing considerably in the total potential and kinetic energies of the disks. Depending on parameters, these modes display the following features: (i) hysteresis (coexistence of the two modes in phase space); (ii) intermingledlike basins of attraction (uncertainty exponent indistinguishable from zero); (iii) two-state on-off intermittency; and (iv) bimodal velocity distributions. Bifurcations are defined by a cross-shaped phase diagram.

Measurement of Impact Ejecta from Regolith Targets in Oblique Impacts

This paper reports the results of experiments on projectile impact into regolith targets at various impact angles. Copper projectiles of 240 mg are accelerated to 197 to 272 m s −1 using an electromagnetic gun. The ejecta are detected by thin Al foil targets as secondary targets, and the resulting holes on the foil are measured to derive the spatial distribution of the ejecta. The ejecta that penetrated the foil are concentrated toward the downrange azimuths of impacting projectiles in oblique impacts. In order to investigate the ejecta velocity distribution, the nondimensional volume of ejecta with velocities higher than a given value is calculated from the spatial distribution. In the case of the vertical impact of the projectile, most ejecta have velocities lower than 24% of the projectile speed (∼50 m s −1), and there are only several ejecta with velocities higher than 72 m s −1. This result confirms the existence of an upper limit to the ejection velocity in the ejecta velocity distribution (Hartmann cutoff velocity) (W. K. Hartmann, 1985, Icarus 63, 69–98). On the other hand, it is found that, in the oblique impacts, there are a large number of ejecta with velocities higher than the Hartmann cutoff velocity. The relative quantity of ejecta above the Hartmann cutoff velocity increases as the projectile impact angle decreases. Taking these results with the results of S. Yamamoto and A. M. Nakamura (1997, Icarus 128, 160–170) from impact experiments using an impact angle of 30°, it can be concluded that the ejecta from these regolith targets exhibit a bimodal velocity distribution. Below a few tens of m s −1, we see the expected velocity distribution of ejecta, but above this velocity we see a separate group of high-velocity ejecta.

Modelling and imaging the Moho transition: the case of the southern Urals

Synthetic seismic modelling is used to test different possible structures and forming processes of the lower crust and Moho. One and two dimensional synthetic seismic modelling of the Moho reflection is carried out to constrain the internal structure of a crust–mantle transition. A reflectivity algorithm was used to calculate the synthetic seismograms for models of the crust–mantle transition consisting of gradient zones and layered sequences. The synthetic seismograms for models consisting of laterally variable velocity structure were calculated by an explicit finite difference wave equation algorithm. The laterally heterogeneous transition models can be achieved by assuming a Moho with different degrees of variable topography or laterally discontinuous layering. The effects of a low velocity surface cover on the seismic signature of deep signals is also analysed. The seismic modelling coupled with stacked images of wide-angle seismic reflection data constrain the case history of the Moho transition beneath the southern Urals. A smooth gradational crust–mantle transition (gradient velocity–depth function) does not predict the seismic features observed in the shot records. The coda of the PmP and the amplitude behaviour of this phase with offset are modelled with a 6 km thick transition zone which consists of approximately 600 m thick, laterally variable layers with a bimodal velocity distribution. The horizontal component stacks of the wide-angle data feature arcuate events suggesting boudin like structures or a boundary with topographic relief. High amplitude sub-Moho reflections support that the structural complexity of the crust–mantle transition can be followed to the upper mantle suggesting eastward dipping structures indicating, either, remnants of an old subduction zone, trapped crustal material within the mantle, or active crust–mantle interactions.

Vibrational and Translational Energy Effects in the Reaction of Ammonia Ions with Water Molecules

The reaction of vibrationally state-selected ammonia ions with deuterated water is investigated with a quadrupole−octopole−quadrupole apparatus. Relative integral reaction cross sections for all ionic products are measured for collisional energies from 0.5 to 10.0 eV (center of mass) and ammonia ion vibrational states 1020-10 and 1122. The predominant charged products have masses of 18 and 21 amu and are shown to be NH2D+ (formal isotope exchange) and D2OH+ (proton transfer), respectively. Small amounts of product are also observed at masses 19, 20, and 22 amu. The cross section for proton transfer decreases with increasing collisional energy, but it increases with increasing internal energy at all collisional energies studied. The cross section for formal isotope exchange increases with increasing collisional energy and increases with increasing internal energy only at low collisional energies. Comparing the reactivity of NH3+(1025) to that of NH3+(1122) (internal energies of 0.60 and 0.63 eV, respectively) shows whether the system is sensitive to the specific vibrational motion, or only to the total amount of internal energy. The present system is shown not to be vibrational-mode selectivethe two internal preparations having comparable reactive cross sections at all collisional energies studied. The projection of the product velocity onto the ion-beam axis is obtained by transforming the experimentally measured product time-of-flight profiles. These velocity profiles contain information regarding energy released into product recoil. The isotope exchange products scatter tightly (0.6 eV, hwhm) about the center of mass and display forward−backward symmetry. The proton-transfer products yield a bimodal velocity distribution with one peak in the backward direction and another on the center of mass. The data observed for the isotope-exchange product indicate a reaction mechanism in which the first step is collision-induced dissociation of the ammonia ion (or water molecule), resulting in a hydrogen (deuterium) atom and an [NH2D2O]+ ([NH3OD]+) complex. This complex may decay to form the products NH2D+ and OD (OH). The majority of the D2OH+ product is formed via direct proton transfer.

Observations of fast anisotropic ion heating, ion cooling, and ion recycling in large-amplitude drift waves

Large-amplitude drift wave fluctuations are observed to cause severe ion temperature oscillations in plasmas of the Caltech Encore tokamak [J. M. McChesney, P. M. Bellan, and R. A. Stern, Phys. Fluids B 3, 3370 (1991)]. Experimental investigations of the complete ion dynamical behavior in these waves are presented. The wave electric field excites stochastic ion orbits in the plane normal (⊥) to B, resulting in rapid ⊥ heating. Ion–ion collisions impart energy along (∥) B, relaxing the ⊥-∥ temperature anisotropy. Hot ions with large orbit radii escape confinement, reaching the chamber wall and cooling the distribution. Cold ions from the plasma edge convect back into the plasma (i.e., recycle), causing further cooling and significantly replenishing the density depleted by orbit losses. The ion–ion collision period τii∼T3/2/n fluctuates strongly with the drift wave phase, due to intense (≈50%) fluctuations in n and T. Evidence for particle recycling is given by observations of bimodal ion velocity distributions near the plasma edge, indicating the presence of cold ions (0.4 eV) superposed atop the hot (4–8 eV) plasma background. These appear periodically, synchronous with the drift wave phase at which ion fluid flow from the wall toward the plasma center peaks. Evidence is presented that such a periodic heat/loss/recycle/cool process is expected in plasmas with strong stochastic heating.

Speed-Dependent Anisotropy Parameters in the UV Photodissociation of Ozone

Resonance-enhanced multiphoton ionization coupled with time-of-flight product imaging has been used to study the O2(3Σg-) + O(3Pj) product channel in the UV photodissociation of ozone at photolysis wavelengths of 226, 230, 240, and 266 nm. For dissociation at 226 and 230 nm the O(3P2) fragment is produced with a strongly bimodal velocity distribution, in keeping with the previous findings of Miller et al., Syage, and Stranges et al. at photolysis wavelengths of 226 and 193 nm. At the longer dissociation wavelengths of 240 and 266 nm, the bimodal velocity distribution becomes less evident in the O(3P2) product. Anisotropy parameters have been determined as a function of the O(3P2) fragment speed. A very similar and clear speed dependence is evident at all photolysis wavelengths considered, with the anisotropy parameters rising steadily as the oxygen atom speed increases. The UV dissociation dynamics of ozone to the channel producing triplet products are discussed in light of this analysis.

The photodissociation of tert-butyl nitrite adsorbed on Ag(111): bimodal velocity distributions of the photoproducts

In this study the photodissociation of physisorbed tert-butyl nitrite, (CH 3) 3CONO, adsorbed on Ag(111) by 355 nm light is investigated at coverages between 0.15 and 50 layers at 85 K. Upon irradiation, time-of-flight spectroscopy showed desorbing NO molecules due to the photodissociation of the tert-butyl nitrite. These molecules show a bimodal velocity distribution with a thermal and a hyperthermal component at all the investigated coverages. The yield and the velocity of the hyperthermal component saturated at a coverage of 5 layers. The conclusion is made that if more than 5 layers are adsorbed the hyperthermal component is produced in the top 5 layers of the film via a direct excitation mechanism. The thermal component consisted of NO photoproducts which had equilibrated to the substrate temperature.

Photodissociation Dynamics of CHF2Cl after Photoexcitation at the Lyman-α Wavelength (121.6 nm)

The collision-free gas-phase photodissociation dynamics of CHF2Cl (HCFC-22) were studied at room temperature using the laser photolysis/laser-induced fluorescence “pump/probe” technique. Lyman-α laser radiation (λ = 121.6 nm) was used both to photodissociate the parent molecule and to detect the nascent H atom products via (2p2P ← 1s2S) laser-induced fluorescence. An absolute H atom quantum yield of ΦH = 0.77 ± 0.13 was determined by a calibration method in which H2O photolysis at 121.6 nm was used as a reference source of well-defined H atom concentrations. The line shapes of the measured H atom Doppler profiles indicate a bimodal velocity distribution suggesting the presence of two different H atom formation pathways in the Lyman-α photodissociation of CHF2Cl.

Photofragment imaging by sections for measuring state-resolved angle-velocity differential cross sections

We describe a two-dimensional (2D) imaging technique for recording state-specific photofragment angle-velocity (θ,v) distributions. In these experiments the photofragment images are recorded as 2D sections of the 3D angular distributions using state-specific ionization in a time-of-flight mass spectrometer. We compare this method to previous methods that record 2D projections of the 3D distribution. The 2D sections represent cartesian flux-velocity maps in the center of mass and are related to angle-velocity differential cross sections by a simple geometric factor. Two studies are highlighted. In the first, new results are presented for the A state photodissociation of CH3I to CH3+I. (θ,v) images are presented for I atom in the 2P3/2 and 2P1/2 spin–orbit states following photodissociation at 266 and 304 nm. The principal result is detection of the weak perpendicular transitions to the 3Q1 state (at 304 nm) and the 1Q state (at 266 nm) that underlie the strong parallel transition to the 3Q0 state. We also report the ratio of cross sections σ⊥/σ∥, the anisotropy and branching ratio for I(2P3/2) and I(2P1/2), and the 3Q0–1Q surface crossing probability. In a second study the photodissociation of O3 to O2(v)+O(3Pj=2,1,0) was measured. A bimodal anisotropic velocity distribution was measured for O(3P) corresponding to maximum in the O2(v) vibrational distribution of v=15 and 27, in general agreement with a previous measurement. The anisotropies of the high- and low-velocity components were measured to be β≊1.1 and 0.4, respectively.