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At least 109 records · Page 6

Deviation from a Maxwellian velocity distribution in regions of interstellar molecular hydrogen

The deviation from a Maxwellian velocity distribution caused by excitation of the J = 2 rotational level of parahydrogen (followed by radiative decay) in a molecular hydrogen gas is investigated. It is noted that inelastic collisions deplete the high-velocity tail of the distribution, while elastic collisions tend to refill it; the resulting steady-state distribution has a small depletion in the tail which slightly reduces the cooling rate of the gas. The elastic-collision transport is approximated by a continuous process, a simplified expression is obtained for the inelastic-collision operator, and the Boltzmann equation is then solved analytically. A correction to the inelastic-collision rate is evaluated, and it is found that the relative magnitude of the effect of tail depletion on the inelastic-collision rate is strongly temperature-dependent. The critical molecular density above which the J = 2 level deexcites by superelastic collisions is shown to be a weak function of temperature.

Gould, R. J.↗

(U) Boundary Conditions for Ejecta Source Models with Stationary Velocity Distributions

We show that certain apparently universal features of the piezoelectric voltage traces measured in HE-driven tin coupon experiments [1, 2] constrain the functional form of any ejecta source model with a stationary velocity distribution. Building on an analytic formalism that has been extensively documented elsewhere [3, 4, 5, 6, 7], we derive simple expressions for V(t 0 a ), V'(t 0 a ), and the discontinuity in V(t break ) where t 0 a is the time of first ejecta arrival at the sensor and t break is the “depletion” time for the fastest particles arriving at the sensor. These three quantities appear to be zero, or nearly so, in the Vo- gan voltage data [1] (modulo noise and any smoothing effects created by the circuit); however, the predicted voltages for this general class of source models do not automatically achieve these conditions unless special boundary conditions are met. Source models which violate these boundary conditions will produce voltage predictions at odds with the measurements. The RMI+SSVD ejecta source model in its current formulation satisfies none of these boundary conditions, and therefore predictions from a stationary-velocity-distribution approximation to the RMI+SSVD source model deviate significantly from the voltage data. This analysis suggests straightforward methods for potentially improving the predictions of the RMI+SSVD ejecta source model. We test this with a simple adjustment to the SSVD and find, as anticipated, the adjustment corrects three properties of the voltage prediction. Furthermore, the adjusted model’s prediction for ejecta mass accumulation at the sensor exhibits a smoother and more gradual rise from the baseline than that produced by the original source model, thereby improving overall model/data agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

2-dimensional ion velocity distributions measured by laser-induced fluorescence above a radio-frequency biased silicon wafer

The dynamics of ions traversing sheaths in low temperature plasmas are important to the formation of the ion energy distribution incident onto surfaces during microelectronics fabrication. Ion dynamics have been measured using laser-induced fluorescence (LIF) in the sheath above a 30 cm diameter, 2.2 MHz-biased silicon wafer in a commercial inductively coupled plasma processing reactor. The velocity distribution of argon ions was measured at thousands of positions above and radially along the surface of the wafer by utilizing a planar laser sheet from a pulsed, tunable dye laser. Velocities were measured both parallel and perpendicular to the wafer over an energy range of 0.4–600 eV. The resulting fluorescence was recorded using a fast CCD camera, which provided resolution of 0.4 mm in space and 30 ns in time. Data were taken at eight different phases during the 2.2 MHz cycle. The ion velocity distributions (IVDs) in the sheath were found to be spatially non-uniform near the edge of the wafer and phase-dependent as a function of height. Several cm above the wafer the IVD is Maxwellian and independent of phase. Experimental results were compared with simulations. The experimental time-averaged ion energy distribution function as a function of height compare favorably with results from the computer model.

36 MATERIALS SCIENCE↗

A theory of local and global processes which affect solar wind electrons. I - The origin of typical 1 AU velocity distribution functions - Steady state theory

A kinetic theory for the velocity distribution of solar wind electrons which illustrates the global and local properties of the solar wind expansion is proposed. By means of the Boltzmann equation with the Krook collision operator accounting for Coulomb collisions, it is found that Coulomb collisions determine the population and shape of the electron distribution function in both the thermal and suprathermal energy regimes. For suprathermal electrons, the cumulative effects of Coulomb interactions are shown to take place on the scale of the heliosphere itself, whereas the Coulomb interactions of thermal electrons occur on a local scale near the point of observation (1 AU). The bifurcation of the electron distribution between thermal and suprathermal electrons is localized to the deep solar corona (1 to 10 solar radii).

Scudder, J. D.↗

General instability criterion of laminar velocity distributions

The present paper describes the results of a stability investigation on symmetrical velocity profiles in a channel and of boundary-layer profiles. The effect of friction was assumed to be vanishing and did not occur in the stability consideration so far as it had been resorted to for preparatory asymptotic considerations. Proceeding on very general premises as regards the form of the velocity distribution, a proof was deduced of the elementary theorem that velocity profiles with inflection points are unstable.

Tollmien, W↗

Cluster Cosmology with the Velocity Distribution Function of the HeCS-SZ Sample

We apply the velocity distribution function (VDF) to a sample of Sunyaev–Zel'dovich (SZ)-selected clusters, and we report preliminary cosmological constraints in the ${\sigma }_{8}$-${{\rm{\Omega }}}_{m}$ cosmological parameter space. The VDF is a forward-modeled test statistic that can be used to constrain cosmological models directly from galaxy cluster dynamical observations. The method was introduced in Ntampaka et al. and employs line-of-sight velocity measurements to directly constrain cosmological parameters; it is less sensitive to measurement error than a standard halo mass function approach. The method is applied to the Hectospec Survey of Sunyaev–Zeldovich-Selected Clusters sample, which is a spectroscopic follow-up of a Planck-selected sample of 83 galaxy clusters. Credible regions are calculated by comparing the VDF of the observed cluster sample to that of mock observations, yielding ${{ \mathcal S }}_{8}$ $\equiv \,{\sigma }_{8}{\left({{\rm{\Omega }}}_{m}/0.3\right)}^{0.25}=0.751\pm 0.037$. These constraints are in tension with the Planck Cosmic Microwave Background TT fiducial value, which lies outside of our 95% credible region, but are in agreement with some recent analyses of large-scale structure that observe fewer massive clusters than are predicted by the Planck fiducial cosmological parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

Scalings of Alfvén-cyclotron and ion Bernstein instabilities on temperature anisotropy of a ring-like velocity distribution in the inner magnetosphere

Here, a ring-like proton velocity distribution with ∂f p (v ⊥ )/∂v ⊥ >0 and which is sufficiently anisotropic can excite two distinct types of growing modes in the inner magnetosphere: ion Bernstein instabilities with multiple ion cyclotron harmonics and quasi-perpendicular propagation and an Alfvén-cyclotron instability at frequencies below the proton cyclotron frequency and quasi-parallel propagation. Recent particle-in-cell simulations have demonstrated that even if the maximum linear growth rate of the latter instability is smaller than the corresponding growth of the former instability, the saturation levels of the fluctuating magnetic fields can be greater for the Alfvén-cyclotron instability than for the ion Bernstein instabilities. In this study, linear dispersion theory and two-dimensional particle-in-cell simulations are used to examine scalings of the linear growth rate and saturation level of the two types of growing modes as functions of the temperature anisotropy T ⊥ /T || for a general ring-like proton distribution with a fixed ring speed of 2v A , where v A is the Alfvén speed. For the proton distribution parameters chosen, the maximum linear theory growth rate of the Alfvén-cyclotron waves is smaller than that of the fastest-growing Bernstein mode for the wide range of anisotropies (1≤T ⊥ /T || ≤7) considered here. Yet the corresponding particle-in-cell simulations yield a higher saturation level of the fluctuating magnetic fields for the Alfvén-cyclotron instability than for the Bernstein modes as long as inline image. Since fast magnetosonic waves with ion Bernstein instability properties observed in the magnetosphere are often not accompanied by electromagnetic ion cyclotron waves, the results of the present study indicate that the ring-like proton distributions responsible for the excitation of these fast magnetosonic waves should not be very anisotropic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Ion velocity distribution at the termination shock: 1-D PIC simulation

The Voyager 2 (V2) plasma observations of the proton temperature downstream of the quasi-perpendicular heliospheric termination shock (TS) showed that upstream thermal solar wind ions played little role in the shock dissipation mechanism and their downstream temperature is an order of magnitude smaller than predicted by MHD Rankine-Hugoniot conditions. While pickup ions (PUI) are generally expected to play an important role in energy dissipation at the shock, the details remain unclear. Here, one-dimensional (1-D) Particle-in-cell (PIC) code is used to examine kinetic properties and downstream velocity distribution functions of pickup ions (the hot supra-thermal component) and solar wind protons (SWs, the cold component) at the perpendicular heliospheric termination shock. The code treats the pickup ions self-consistently as a third component. Present results show that: (1) both of the incident SWs and PUIs can be separated into two parts: reflected (R) ions and directly transmitted (DT) ions, the energy gain of the R ions at the shock front is much larger than that of the DT ions; (2) the fraction of reflected SWs and their downstream temperature decrease with the relative percentage PUI%; (3) no matter how large the PUI% is, the downstream ion velocity distribution function always can be separated into three parts: 1. a high energy tail (i.e. the wings) dominated by the reflected PUIs, 2. a low energy core mainly contributed by the directly transmitted SWs, and 3. a middle energy part which is a complicated superposition of reflected SWs and directly transmitted PUIs. The significance of the presence of pickup ions on shock front micro-structure and nonstationarity is also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

REVISED MODEL OF THE STEADY-STATE SOLAR WIND HALO ELECTRON VELOCITY DISTRIBUTION FUNCTION

A recent study discussed the steady-state model for solar wind electrons during quiet time conditions. The electrons emanating from the Sun are treated in a composite three-population model—the low-energy Maxwellian core with an energy range of tens of eV, the intermediate ∼10{sup 2}–10{sup 3} eV energy-range (“halo”) electrons, and the high ∼10{sup 3}–10{sup 5} eV energy-range (“super-halo”) electrons. In the model, the intermediate energy halo electrons are assumed to be in resonance with transverse EM fluctuations in the whistler frequency range (∼10{sup 2} Hz), while the high-energy super-halo electrons are presumed to be in steady-state wave–particle resonance with higher-frequency electrostatic fluctuations in the Langmuir frequency range (∼10{sup 5} Hz). A comparison with STEREO and WIND spacecraft data was also made. However, ignoring the influence of Langmuir fluctuations on the halo population turns out to be an unjustifiable assumption. The present paper rectifies the previous approach by including both Langmuir and whistler fluctuations in the construction of the steady-state velocity distribution function for the halo population, and demonstrates that the role of whistler-range fluctuation is minimal unless the fluctuation intensity is arbitrarily raised. This implies that the Langmuir-range fluctuations, known as the quasi thermal noise, are important for both halo and super-halo electron velocity distribution.

79 ASTRONOMY AND ASTROPHYSICS↗

Velocity Distribution in the Boundary Layer of a Submerged Plate

This report deals with the measurement of the velocity distribution of the air in the velocity of a plate placed parallel to the air flow. The measurements took place in a small wind tunnel where the diameter of the entrance cone is 30 cm and the length of the free jet between the entrance and exit cones is about 2.5 m. The measurements were made in the free jet where the static pressure was constant, which was essential for the method of measurement used.

Hansen, M↗

Dependence of dark matter - electron scattering on the galactic dark matter velocity distribution

The rate of dark matter-electron scattering depends on the underlying velocity distribution of the dark matter halo. Importantly, dark matter-electron scattering is particularly sensitive to the high-velocity tail, which differs significantly amongst the various dark matter halo models. In this work, we summarize the leading halo models and discuss the various parameters which enter them. We recommend updated values for these parameters based on recent studies and measurements. Furthermore, we quantify the dependence of the dark matter-electron scattering rate on the choice of halo model and parameters, and demonstrate how these choices propagate to the predicted cross-section limits. The rate is most sensitive to changes in the circular velocity v 0 ; in silicon targets, we find that the changes in the rate predictions can range from Script $\mathcal{O}$(0.01%) to Script $\mathcal{O}$(100%) for contact interactions and Script $\mathcal{O}$(10%) to Script $\mathcal{O}$(100%) for long-range interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurements of parallel electron velocity distributions using whistler wave absorption

We describe a diagnostic to measure the parallel electron velocity distribution in a magnetized plasma that is overdense ({omega}{sub pe} > {omega}{sub ce}). This technique utilizes resonant absorption of whistler waves by electrons with velocities parallel to a background magnetic field. The whistler waves were launched and received by a pair of dipole antennas immersed in a cylindrical discharge plasma at two positions along an axial background magnetic field. The whistler wave frequency was swept from somewhat below and up to the electron cyclotron frequency {omega}{sub ce}. As the frequency was swept, the wave was resonantly absorbed by the part of the electron phase space density which was Doppler shifted into resonance according to the relation {omega}-k{sub ||v||} = {omega}{sub ce}. The measured absorption is directly related to the reduced parallel electron distribution function integrated along the wave trajectory. The background theory and initial results from this diagnostic are presented here. Though this diagnostic is best suited to detect tail populations of the parallel electron distribution function, these first results show that this diagnostic is also rather successful in measuring the bulk plasma density and temperature both during the plasma discharge and into the afterglow.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Turbulence Model Study for Pressure and Velocity Distributions for Molten Salts in a Crossflow Tube Bundle

Empirical pressure drop correlations for various compositions of molten salts in crossflow across tube bundles/banks are limited due to the scarcity of experimental data for these fluids. This lack of experimental data presents a limitation when designing heat exchangers for Molten Salt Reactors (MSRs) that utilize cross-flow configurations with turbulent molten salts flowing in the shell side. In an effort to provide a starting point for future design and experimental work, a computational fluid dynamics (CFD) campaign is being conducted to estimate pressure drops over a range of Reynolds numbers, pitch to diameter ratios, and for both staggered and in-line tube banks. In an effort to continue this work, the study of various turbulence models were conducted to determine the applicability for steady RANS simulations. An in-line tube bank with FLiBe (LiF-BeF{sub 2}), a frequently selected molten salt in MSRs, was selected for these simulations. The estimated pressure drops and pressure and velocity distributions for each turbulence model was compared to determine the applicability. The k-ε turbulence model family was found to be the most appropriate model for steady Reynolds averaged Navier Stokes within this type of domain. Difference turbulence models were investigated for simulation of molten salt experiencing crossflow within an in-line tube bundle. The flow was simulated using a steady RANS formulation with different families of turbulence models. The different turbulence models provide a view of this specific flow behavior potential requirements and applicable for steady RANS. Of particular note, the k-ε models were able to converge easily within this domain. The predicted behavior for both models were observed to be mostly similar for both velocity and pressure distributions. Whereas, k-ω SST and SA models did not converge well and had observable differences for the predictions of pressure and velocity distributions. The global behaviors were generally similar, but the variations occurring suggest k-ω SST and SA turbulence models are not useful in the steady RANS formulation of this domain. When comparing to the empirical pressure drop, each turbulence model resulted in overpredictions ranging from 8.7% and 19.75% difference. The standard low-Re k-ε model having the lowest difference is likely the better model for simplified predictions for pressure drops. Further investigations will be conducted to determine the convergence issues for the k-ω SST and SA turbulence models. These might be due to the flow geometry or potentially a revision of the meshing is needed. The flow behavior may not be resolved using these models in a steady formulation due to inherent unsteadiness of the flow. (authors)

42 ENGINEERING↗

Planar laser-induced fluorescence system for spatiotemporal ion velocity distribution function measurements

In this work, we present a planar laser-induced fluorescence (PLIF) system for measuring two-dimensional (2D), spatiotemporally resolved ion velocity distribution functions (IVDFs). A continuous-wave tunable diode laser produces a laser sheet that irradiates the plasma, and the resulting fluorescence is captured by an intensified CCD (ICCD) camera. Fluorescence images recorded at varying laser wavelengths are converted into 2D IVDFs using the Doppler shift principle. The developed diagnostic is implemented in an electron beam generated E × B plasma with a bulk plasma density of $\sim\!\!{10^{10}}{\text{c}}{{\text{m}}^{ - 3}}$ . The developed diagnostic is validated against a conventional single-point LIF method using photomultiplier tube-based detection, while significantly reducing the total measurement time by the number of spatial positions measured. The time-resolving capability of this diagnostic is tested by oscillating the plasma between two nominal operating modes with different density profiles and triggering the ICCD camera by the externally driven plasma oscillation. The measured 2D IVDF maps reveal several signatures of ion dynamics in this plasma source, including radially outflowing ions across the electric field and anomalous ion heating at the periphery, consistent with recent kinetic simulations and theoretical studies. A possible correlation between these ion kinetic features and rotating spoke structures is discussed.

E×B plasma↗

The velocity distribution of pickup He{sup +} measured at 0.3 AU by MESSENGER

During its interplanetary trajectory in 2007-2009, the MErcury Surface, Space ENvrionment, GEochemistry, and Ranging (MESSENGER) spacecraft passed through the gravitational focusing cone for interstellar helium multiple times at a heliocentric distance R ≈ 0.3 AU. Observations of He{sup +} interstellar pickup ions made by the Fast Imaging Plasma Spectrometer sensor on MESSENGER during these transits provide a glimpse into the structure of newly formed inner heliospheric pickup-ion distributions. This close to the Sun, these ions are picked up in a nearly radial interplanetary magnetic field. Compared with the near-Earth environment, pickup ions observed near 0.3 AU will not have had sufficient time to be energized substantially. Such an environment results in a nearly pristine velocity distribution function that should depend only on pickup-ion injection velocities (related to the interstellar gas), pitch-angle scattering, and cooling processes. From measured energy-per-charge spectra obtained during multiple spacecraft observational geometries, we have deduced the phase-space density of He{sup +} as a function of magnetic pitch angle. Our measurements are most consistent with a distribution that decreases nearly monotonically with increasing pitch angle, rather than the more commonly modeled isotropic or hemispherically symmetric forms. These results imply that pitch-angle scattering of He{sup +} may not be instantaneous, as is often assumed, and instead may reflect the velocity distribution of initially injected particles. In a slow solar wind stream, we find a parallel-scattering mean free path of λ {sub ||} ∼ 0.1 AU and a He{sup +} production rate of ∼0.05 m{sup –3} s{sup –1} within 0.3 AU.

79 ASTRONOMY AND ASTROPHYSICS↗