Analytic solution to charge-exchange source terms between Maxwellian and kappa-distributed velocity distributions in the heliosphere
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Anthony Michael DeStefano↗
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Non-Maxwellian velocity distribution functions associated with steep temperature gradients in the solar transition region. Paper 1: Estimate of the electron velocity distribution functions
It was shown that, in the presence of the steep temperature gradients characteristic of EUV models of the solar transition region, the electron and proton velocity distribution functions are non-Maxwellian and are characterized by high energy tails. The magnitude of these tails are estimated for a model of the transition region and the heat flux is calculated at a maximum of 30 percent greater than predicted by collision-dominated theory.
Roussel-Dupre, R.↗
Non-Maxwellian velocity distribution functions associated with steep temperature gradients in the solar transition region. I - Estimate of the electron velocity distribution functions. II - The effect of non-Maxwellian electron distribution functions on ionization equilibrium calculations for carbon, nitrogen and oxygen
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Roussel-Dupre, R.↗
Observations of Counter-Streaming Ion Velocity Distributions in LLBL
We analyze ion velocity distributions observed by Interball-Tail at two LLBL crossings under southward and variable magnetosheath magnetic field. These magnetic conditions lead to highly structured LLBL. D-shape ion velocity distributions were observed within LLBL structures along with other reconnection signatures. Another type of the ion velocity distributions observed within LLBL structures consists of two counter-streaming magnetosheath-type components. We consider two possible scenarios that may lead to development of these counterstreaming ion components: reflection of transmitted magnetosheath ions from the ionosphere and creation of these velocity distributions during formation of the LLBL. We argue that observed counter-streaming component could not be due to ionospheric reflection. The observations of these ion velocity distributions are in favor of the multiple reconnections between magnetosheath and magnetospheric flux tubes.
Vaisberg, O. L.↗
Tip vortices - Velocity distributions
Flow field velocity distribution at rotating wing devices tip vortices
Chigier, N. A.↗
The velocity distribution of cometary hydrogen - Evidence for high velocities?
The Hamilton Echelle spectrograph on the 3-m Shane telescope at Lick Observatory was used to obtain high-velocity and spatial resolution 2D spectra of H-alpha 6563-A emission in Comets Austin and Levy. The presence of the components expected from water dissociation and collisional thermalization in the inner coma is confirmed by the hydrogen velocity distribution. In Comet Austin, the potential high-velocity hydrogen includes velocities of up to about 40 km/s and is spatially symmetric with respect to the nucleus. In Comet Levy, the high-velocity hydrogen reaches velocities of up to 50 km/s and is situated exclusively on the sunward side of the nucleus. The two distinct signatures of high-velocity hydrogen imply two distinct sources.
Brown, Michael E.↗
Ion velocity distributions in the vicinity of the current sheet in Earth's distant magnetotail
Observations of the three-dimensional velocity distributions of positive ions and electrons have been recently gained for the first time in Earth's distant magnetotail with the Galileo and Geotail spacecraft. For this brief discussion of these exciting results the focus is on the overall character of the ion velocity distributions during substorm activity. The ion velocity distributions within and near the magnetotail current sheet are not accurately described as convecting, isotropic Maxwellians. The observed velocity distributions are characterized by at least two robust types. The first type is similar to the 'lima bean'-shaped velocity distributions that are expected from the nonadiabatic acceleration of ions which execute Speiser-type trajectories in the current sheet. The second distribution is associated with the presence of cold ion beams that presumably also arise from the acceleration of plasma mantle ions in the electric and weak magnetic fields in the current sheet. The ion velocity distributions in a magnetic field structure that is similar to that for plasmoids are also examined. Again the velocity distributions are not Maxwellian but are indicative of nonadiabatic acceleration. An example of the pressure tensor within the plasmoid-like event is also presented because it is anticipated that the off-diagonal elements are important in a description of magnetotail dynamics. Thus our concept of magnetotail dynamics must advance from the present assumption of co-moving electron and ion Maxwellian distributions into reformulations in terms of global kinematical models and nonadiabatic particle motion.
Frank, L. A.↗
Velocity distributions among colliding asteroids
The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.
Bottke, William F., Jr.↗
Behaviour of ion velocity distributions for a simple collision model
Calculation of the ion velocity distributions for a weakly ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV/m. This shape persists for one to two hours after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fields. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.
St-Maurice, J.-P.↗
Detection of bump-on-tail reduced electron velocity distributions at the electron foreshock boundary
Reduced velocity distributions are derived from three-dimensional measurements of the velocity distribution of electrons in the 7 to 500 eV range in the electron foreshock. Bump-on-tail reduced distributions are presented for the first time at the foreshock boundary consistent with Filbert and Kellogg's proposed time-of-flight mechanism for generating the electron beams. In a significant number of boundary crossings, bump-on-tail reduced distributions were found in consecutive 3 sec measurements made 9 sec apart. It is concluded that, although the beams are linearly unstable to plasma waves according to the Penrose criterion, they persist on a time scale of 3 to 15 sec.
Fitzenreiter, R. J.↗
Detection of bump-on-tail reduced electron velocity distributions at the electron foreshock boundary
Reduced velocity distributions are derived from three-dimensional measurements of the velocity distribution of electrons in the 7 to 500 eV range in the electron foreshock. Bump-on-tail reduced distributions are presented for the first time at the foreshock boundary consistent with Filbert and Kellogg's proposed time-of-flight mechanism for generating the electron beams. In a significant number of boundary crossings, bump-on-tail reduced distributions were found in consecutive 3 sec measurements made 9 sec apart. It is concluded that, although the beams are linearly unstable to plasma waves according to the Penrose criterion, they persist on a time scale of 3 to 15 sec. Previously announced in STAR as N84-22518
Fitzenreiter, R. J.↗
Ion Velocity Distributions Within LLBL and Their Possible Implication to Multiple Reconnections
We analyze two LLBL crossings made by Interball Tail satellite under southward or variable magnetosheath magnetic field: one crossing on the flank of the magnetosphere, and another one closer to the subsolar point. Three different types of ion velocity distributions within LLBL are observed: (a) D-shaped distributions, (b) ion velocity distributions consisting of two counter-streaming components of magnetosheath-ty and (c) distributions with three components one of which has nearly zero parallel velocity and two counter-streaming components. Only the (a) type fits to the single magnetic flux tube formed by reconnection between magnetospheric and magnetosheath magnetic fields. We argue that two counter-streaming magnetosheath-like ion components observed by Interball within LLBL cannot be explained by the reflection of the ions from the magnetic mirror deeper within magnetosphere. Types (b) and (c) ion velocity distributions would form within spiral magnetic flux tube consisting of a mixture of alternating segments originating from the magnetosheath and from magnetospheric plasma. The shapes of ion velocity distributions and their evolution with decreasing number density in LLBL indicate that a significant part of LLBL is located on magnetic field lines of long spiral flux tube islands at the magnetopause, as has been proposed and found to occur in magnetopause simulations. We consider these observations as evidence for multiple reconnection X-ray lines between magnetosheath and magnetospheric flux tubes.
Vaisberg, O. L.↗
The Velocity Distribution of Isolated Radio Pulsars
We infer the velocity distribution of radio pulsars based on large-scale 0.4 GHz pulsar surveys. We do so by modelling evolution of the locations, velocities, spins, and radio luminosities of pulsars; calculating pulsed flux according to a beaming model and random orientation angles of spin and beam; applying selection effects of pulsar surveys; and comparing model distributions of measurable pulsar properties with survey data using a likelihood function. The surveys analyzed have well-defined characteristics and cover approx. 95% of the sky. We maximize the likelihood in a 6-dimensional space of observables P, dot-P, DM, absolute value of b, mu, F (period, period derivative, dispersion measure, Galactic latitude, proper motion, and flux density). The models we test are described by 12 parameters that characterize a population's birth rate, luminosity, shutoff of radio emission, birth locations, and birth velocities. We infer that the radio beam luminosity (i) is comparable to the energy flux of relativistic particles in models for spin-driven magnetospheres, signifying that radio emission losses reach nearly 100% for the oldest pulsars; and (ii) scales approximately as E(exp 1/2) which, in magnetosphere models, is proportional to the voltage drop available for acceleration of particles. We find that a two-component velocity distribution with characteristic velocities of 90 km/ s and 500 km/ s is greatly preferred to any one-component distribution; this preference is largely immune to variations in other population parameters, such as the luminosity or distance scale, or the assumed spin-down law. We explore some consequences of the preferred birth velocity distribution: (1) roughly 50% of pulsars in the solar neighborhood will escape the Galaxy, while approx. 15% have velocities greater than 1000 km/ s (2) observational bias against high velocity pulsars is relatively unimportant for surveys that reach high Galactic absolute value of z distances, but is severe for spatially bounded surveys; (3) an important low-velocity population exists that increases the fraction of neutron stars retained by globular clusters and is consistent with the number of old objects that accrete from the interstellar medium; (4) under standard assumptions for supernova remnant expansion and pulsar spin-down, approx. 10% of pulsars younger than 20 kyr will appear to lie outside of their host remnants. Finally, we comment on the ramifications of our birth velocity distribution for binary survival and the population of inspiraling binary neutron stars relevant to some GRB models and potential sources for LIGO.
Arzoumanian, Z.↗
PLIF Temperature and Velocity Distributions in Laminar Hypersonic Flat-plate Flow
Rotational temperature and velocity distributions have been measured across a hypersonic laminar flat-plate boundary layer, using planar laser-induced fluorescence. The measurements are compared to a finite-volume computation and a first-order boundary layer computation, assuming local similarity. Both computations produced similar temperature distributions and nearly identical velocity distributions. The disagreement between calculations is ascribed to the similarity solution not accounting for leading-edge displacement effects. The velocity measurements agreed to within the measurement uncertainty of 2 % with both calculated distributions. The peak measured temperature was 200 K lower than the computed values. This discrepancy is tentatively ascribed to vibrational relaxation in the boundary layer.
OByrne, S.↗
Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data
This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.
Gurgiolo, Chris↗
Ion velocity distributions in the high-latitude ionosphere
The theory and observations relating to ion velocity distributions in the high-latitude F region are reviewed. The review covers three basic aspects, including methods for calculating ion velocity distributions, experimental evidence for the existence of non-Maxwellian ion velocity distributions, and the ionospheric consequences of non-Maxwellian distributions. Specific topics covered include closed form solutions to Boltzmann's equation for a simple collision model, series solutions to the Boltzmann equation for more general collision models, retarding potential analyzer measurements, excitation of VLF electrostatic emissions, ion-neutral reaction rates, and transport effects.
St-Maurice, J.-P.↗
Velocity distributions of H and OH produced through solar photodissociation of H2O
The calculated velocity distributions of atomic hydrogen and hydroxyl radicals produced through solar photodissociation of gaseous water molecules are presented. Under collisionless conditions, the calculation was carried out using the most recent available data for the production of H and OH through photodissociation of H2O from its dissociation onset throughout the EUV region. Because the lack of data in certain spectral regions, only upper and lower bounds to the velocity distributions can be obtained. The results show that the H atoms and OH radicals produced exhibit multiple velocity groups. Since most of the current cometary modeling uses a single velocity of 20 km/s associated with the photodissociation of H2O, the present results may be useful in interpreting the many peaks observed in the velocity distributions of cometary atomic hydrogen.
Wu, C. Y. Robert↗
The ellipsoidal velocity distribution function
Relation between ellipsoidal velocity distribution function and macroscopic flow equations
Stankiewicz, N.↗