The relation between transverse and radial velocity distributions for observations of an isotropic velocity field
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Effect of velocity distributions on power-limited propulsion system
Because of spacecraft orbital motion about the Earth, a much higher flux of meteoroids is expected to strike spacecraft surfaces that face in the direction of spacecraft motion (apex direction) than would strike apex facing or trailing edge surfaces. Impact velocities are also higher on apex facing surfaces compared to antapex facing surfaces which futher increases the apex/antapex ratio of spatial density of impact craters of a given size. Measurements of the areal densities of impact craters on the different LDEF surfaces should give important clues about the velocity distribution, and therefore the origins, of meteoroids. Preliminary results appear to support the meteoroid velocity distributions derived by Erickson and by Kessler, which would lead to a mean impact velocity on the LDEF spacecraft of about 19 km/s.
Steady state ion velocity distribution functions for partially ionized gas not in thermal equilibrium, noting small distortion
Previous work on electron heating mechanisms operating at the supercritical earth's bow shock is extended to the generally lower Mach number interplanetary shocks. This is done by studying electron velocity distributions observed both upstream and downstream of interplanetary shocks observed by ISEE 3 between August 1978 and December 1979. It is found that perpendicular heating accompanied by little or no parallel heating occurs at the weaker shocks but that parallel heating is dominant for the stronger shocks. When perpendicular heating is dominant, downstream velocity distributions are for the most part Gaussian at low energies (core) and Lorentzian at high energies (halo). When parallel heating is dominant, however, these distributions are flat-topped at low energies, having power law extensions to higher energies. At the weaker shocks, the observations are consistent with electron heating resulting from conservation of the magnetic moment, whereas at the stronger shocks the heating is quite similar to that observed at the earth's bow shock.
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.
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.
Effect of meteoroid flux velocity distribution and angle of impact on design of spacecraft meteoroid protection systems
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.
Low density plasma electron velocity distribution deviation due to Maxwellian photon radiation resulting from inelastic collisions with atoms
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).
Kinetic theory-plasma dynamics theory calculations of magnetospheric solar wind proton velocity distribution as function of particle speed
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.
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.
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.
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.
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.
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.