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Results for “DISTRIBUTION FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

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.↗
NASA NTRS2019

A Comparative Study on Computation of Cumulative Distribution Function in Predicting Time of Failure of Engineering Systems

Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuna and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time . Results for ToF estimation using Acuna's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition. Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.

Hazard Zone↗
NASA NTRS1995

A review of solar wind ion and electron plasma distribution functions: Present understanding and Ulysses results

Our present understanding of the distribution functions of the solar wind ion and electron thermal/suprathermal populations will be reviewed covering selected theoretical and observational topics. Roughly half the review will be devoted to recent discoveries (since Solar Wind 7). Among recent results are those of the Ulysses mission. The SWICS experiment observed pick-up protons and alpha particles, and acceleration of these particles at interplanetary shocks. Positive ion phenomena observed by SWOOPS include enhanced proton-alpha particle differential streaming both: (1) at high latitudes; and (2) in the ecliptic beyond 1 AU in the vicinity of shocks. The SWOOPS positive ion observations also demonstrate relative constancy of the entropy per proton at high latitudes beyond about 2.5 AU. Double beaming in both protons and alphas is observed by SWOOPS on either side of the current sheet, but not within; a possible explanation is reconnection at the edge of the current sheet. SWOOPS observed bi-directional streaming of electrons beyond 2 AU not only within Coronal Mass Ejections, but also upstream of corotating interplanetary shocks. Latitudinal and radial gradients of Ulysses electron core and halo temperatures will be discussed, as will work in progress on the three dimensional (in velocity space) properties of ion distributions.

Goldstein, B. E.↗
NASA NTRS1991

Probability distribution functions in turbulent convection

Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.

Balachandar, S.↗
NASA NTRS1991

Probability distribution functions in turbulent convection

Results of an extensive investigation of probability distribution functions (pdf's) for Rayleigh-Benard convection, in the hard turbulence regime, are presented. It is seen that the pdf's exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to universality is presented.

Balachandar, S.↗
NASA NTRS2016

Electron Distribution Functions in the Diffusion Region of Asymmetric Magnetic Reconnection

We study electron distribution functions in a diffusion region of antiparallel asymmetric reconnection by means of particle-in-cell simulations and analytical theory. At the electron stagnation point, the electron distribution comprises a crescent-shaped population and a core component. The crescent-shaped distribution is due to electrons coming from the magnetosheath toward the stagnation point and accelerated mainly by electric field normal to the current sheet. Only a part of magnetosheath electrons can reach the stagnation point and form the crescent-shaped distribution that has a boundary of a parabolic curve. The penetration length of magnetosheath electrons into the magnetosphere is derived. We expect that satellite observations can detect crescent-shaped electron distributions during magnetopause reconnection.

Electron↗
NASA NTRS1982

An instrument for rapidly measuring plasma distribution functions with high resolution

An instrument which can rapidly measure plasma particle distribution functions has been developed based upon recent innovations in electrostatic analyzer design and position sensitive particle detection. The new analyzer uses a quadrispherical geometry, but has a completely uniform 360 deg fan-shaped field of view. The polar angular distribution of entering particles is spatially imaged onto a position sensitive detector at the annular exit aperture after a deflection through 90 deg. Several methods of position sensitive detection have been successfully used in conjunction with this analyzer. The simplest is individual channel multipliers spaced around the annular exit. Microchannel plate electron multipliers permit greater position resolution to be obtained, and a detector using microchannel plates followed by a resistive anode image converter obtains angular resolution of about one degree, i.e., 360 individual angle pixels. Instruments of this type were flown on a sounding rocket in early 1982 and will be included on the Giotto comet mission and the AMPTE ion release module (IRM).

Carlson, C. W.↗
NASA NTRS1976

Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique.

Bathke, C. G.↗
NASA NTRS1994

A Monte Carlo simulation of the effect of ion self-collisions on the ion velocity distribution function in the high-latitude F-region

Non-Maxwellian ion velocity distribution functions have been theoretically predicted and confirmed by observations, to occur at high latitudes. These distributions deviate from Maxwellian due to the combined effect of the E x B drift and ion-neutral collisions. At high altitude and/or for solar maximum conditions, the ion-to-neutral density ratio increases and, hence, the role of ion self-collisions becomes appreciable. A Monte Carlo simulation was used to investigate the behavior of O(+) ions that are E x B-drifting through a background of neutral O, with the effect of O(+) (Coulomb) self-collisions included. Wide ranges of the ion-to-neutral density ratio n(sub i)/n(sub n) and the electrostatic field E were considered in order to investigate the change of ion behavior with solar cycle and with altitude. For low altitudes and/or solar minimum (n(sub i)/n(sub n) less than or equal to 10(exp -5)), the effect of self-collisions is negligible. For higher values of n(sub i)/n(sub n), the effect of self-collisions becomes significant and, hence, the non-Maxwellian features of the O(+) distribution are reduced. The Monte Carlo results were compared to those that used simplified collision models in order to assess their validity. In general, the simple collision models tend to be more accurate for low E and for high n(sub i)/n(sub n).

Barghouthi, I. A.↗
NASA NTRS1983

Electron distribution functions in a current sheet

Using a novel directional velocity analyzer the electron distribution function f(v,r,t) is measured in a magnetic-field-line reconnection experiment. Runaway electrons are observed inside the current sheet, a result important for transport processes and instabilities.

Stenzel, R. L.↗