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NASA NTRS1991

The modified plasma dispersion function

The modified plasma dispersion function (MPDF), based on the generalized Lorentzian (kappa) particle distribution function, is introduced, and a comprehensive set of graphs of the real and imaginary parts of the MPDF is presented. For any positive integral value of kappa, MPDF is calculated in closed form as a finite series. It is demonstrated how the MPDF approaches the plasma dispersion function in the limit as kappa yields infinity, a result to be expected since the kappa distribution function formally approaches the Maxwellian as kappa yields infinity. It is concluded that the MPDF can provide a tool in studying microinstabilities in plasmas when the particle distribution function is not only the standard generalized Lorentzian, but also of the Lorentzian type, including the loss-cone, bi-Lorentzian, and product bi-Lorentzian distributions.

Summers, Danny↗
NASA NTRS2004

Plasma Dispersion Function for the Kappa Distribution

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

Podesta, John J.↗
NASA NTRS1973

Approximations to the plasma dispersion function

Two simple approximations to the plasma dispersion function are analyzed and compared. One, is the resonance distribution approximation which is based on the utilization of resonance velocity distributions; the other, is the two-pole approximation proposed by Fried, Hedrick, and McCune (1968). The approximations are applied to Landau and whistler waves. Possible means of improving the two-pole approximation are discussed.

Brinca, A. L.↗
NASA NTRS1988

Approximation of the dielectric properties of Maxwellian plasmas - Dispersion functions and physical constraints

The dielectric properties of Maxwellian plasmas are approximated using high Pade approximants to the dispersion function and direct approximation of the distribution. Physical constraints on permissible approximations are discussed, and it is found that some previously published results can lead to predictions of qualitatively incorrect wave properties, including unphysical negative damping. Approximate dispersion functions for Maxwellian distributions are given explicitly, and some of the effects of these approximations on the resulting dispersion are discussed. The approximations discussed here are of use both in analytical work and in accelerating large-scale numerical computations.

Robinson, P. A.↗
NASA NTRS1972

Approximations to the plasma dispersion function

Linear wave propagation in hot collisionless plasmas is described by the linearized Vlasov and Maxwell equations. In uniform media, the utilization of spatial and temporal transforms of those equations leads to the consideration of integrals of the Hilbert transform type. Analysis and comparison of two simple approximations are provided based on the utilization of resonance velocity distributions. Application is then made to the Landau and whistler waves, along with a discussion of the results, and commentary on possible improvements.

Brinca, A. L.↗
NASA NTRS2010

Reinforced Thermoplastic Polyimide with Dispersed Functionalized Single Wall Carbon Nanotubes

Molecular pi-complexes were formed from pristine HiPCO single-wall carbon nanotubes (SWCNTs) and 1-pyrene- N-(4- N'-(5-norbornene-2,3-dicarboxyimido)phenyl butanamide, 1. Polyimide films were prepared with these complexes as well as uncomplexed SWCNTs and the effects of nanoadditive addition on mechanical, thermal, and electrical properties of these films were evaluated. Although these properties were enhanced by both nanoadditives, larger increases in tensile strength and thermal and electrical conductivities were obtained when the SWCNT/1 complexes were used. At a loading level of 5.5 wt %, the Tg of the polyimide increased from 169 to 197 C and the storage modulus increased 20-fold (from 142 to 3045 MPa). The addition of 3.5 wt % SWCNT/1 complexes increased the tensile strength of the polyimide from 61.4 to 129 MPa; higher loading levels led to embrittlement and lower tensile strengths. The electrical conductivities (DC surface) of the polyimides increased to 1 x 10(exp -4) Scm(exp -1) (SWCNT/1 complexes loading level of 9 wt %). Details of the preparation of these complexes and their effects on polyimide film properties are discussed.

Lebron-Colon, Marisabel↗
NASA NTRS2012

On the Ice Nucleation Spectrum

This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be reconciled, and that is suitable for application in atmospheric modeling studies.

Barahona, D.↗
NASA NTRS1991

Landau damping in space plasmas

The Landau damping of electrostatic Langmuir waves and ion-acoustic waves in a hot, isotropic, nonmagnetized, generalized Lorentzian plasma is analyzed using the modified plasma dispersion function. Numerical solutions for the real and imaginary parts of the wave frequency omega sub 0 - (i)(gamma) have been obtained as a function of the normalized wave number (k)(lambda sub D), where lambda sub D is the electron Debye length. For both particle distributions the electrostatic modes are found to be strongly damped at short wavelengths. At long wavelengths, this damping becomes less severe, but the attenuation of Langmuir waves is much stronger for a generalized Lorentzian plasma than for a Maxwellian plasma. It is concluded that Landau damping of ion-acoustic waves is only slightly affected by the presence of a high energy tail, but is strongly dependent on the ion temperature.

Thorne, Richard M.↗
NASA NTRS1992

A new tool for analyzing microinstabilities in space plasmas modeled by a generalized Lorentzian (kappa) distribution

The modified plasma dispersion function Z* sub kappa (xi) based on the generalized Lorentzian distribution, which was introduced by Summers and Thorne (1991), is used to analyze three classical problems of plasma physics. These include the Landau damping of Langmuir waves, the ion acoustic instability in a current-carrying plasma, and the cyclotron resonant instability of electromagnetic R mode waves propagating parallel to an ambient magnetic field. It was found that, in each case, the results for a generalized Lorentzian plasma can differ significantly from those for a Maxwellian plasma. It is suggested that previous calculations based on a Maxwellian plasma distribution function Z(xi) have to be reexamined.

Summers, Danny↗
NASA NTRS2022

Quantifying urban, industrial, and background changes in NO2 during the COVID-19 lockdown period based on TROPOMI satellite observations

The COVID-19 lockdown had a large impact on anthropogenic emissions of air pollutants and particularly on nitrogen dioxide (NO 2 ). While the overall NO 2 decline over some large cities is well-established, understanding the details remains a challenge since multiple source categories contribute. In this study, a new method of isolation of three components (background NO 2 , NO 2 from urban sources, and NO 2 from industrial point sources) is applied to estimate the impact of the COVID-19 lockdown on each of them. The approach is based on fitting satellite data by a statistical model with empirical plume dispersion functions driven by a meteorological reanalysis. Population density and surface elevation data as well as coordinates of industrial sources were used in the analysis. The tropospheric NO 2 vertical column density (VCD) values measured by the Tropospheric Monitoring Instrument (TROPOMI) on board the Sentinel-5 Precursor over 261 urban areas for the period from 16 March to 15 June 2020 were compared with the average VCD values for the same period in 2018 and 2019. While the background NO 2 component remained almost unchanged, the urban NO 2 component declined by −18 % to −28 % over most regions. India, South America, and a part of Europe (particularly, Italy, France, and Spain) demonstrated a −40 % to −50 % urban emission decline. In contrast, the decline over urban areas in China, where the lockdown was over during the analysed period, was, on average, only -4.4± 8 %. Emissions from large industrial sources in the analysed urban areas varied greatly from region to region from -4.8 ± 6 % for China to -40 ± 10 % for India. Estimated changes in urban emissions are correlated with changes in Google mobility data (the correlation coefficient is 0.62) confirming that changes in traffic were one of the key elements in the decline in urban NO2 emissions. No correlation was found between changes in background NO2 and Google mobility data. On the global scale, the background and urban components were remarkably stable in 2018, 2019, and 2021, with averages of all analysed areas all being within ±2.5 % and suggesting that there were no substantial drifts or shifts in TROPOMI data. The 2020 data are clearly an outlier: in 2020, the mean background component for all analysed areas (without China) was -6.0 % ± 1.2 % and the mean urban component was -26.7 ± 2.6 % or 20σ below the baseline level from the other years.

COVID-19↗
NASA NTRS1990

Systematic methods for calculation of the dielectric properties of arbitrary plasmas

In the novel approach presented for calculating the dispersion integrals needed for determining plasma dielectric properties, the dispersion integrals for an arbitrary distortion function with a continuous derivative are systematically expanded in terms of a set of orthogonal functions whose corresponding dispersion functions are already known. This general approach is, on the one hand, implemented for unmagnetized plasmas, and on the other generalized to treat relativistic and magnetized plasmas. The method allows the systematic and efficient calculation of dispersion integrals, for the cases of either real or complex arguments.

Robinson, P. A.↗
NASA NTRS1977

Propagation along azimuthally magnetized ferrite-loaded circular waveguides

The paper describes the modal dispersion characteristics of electromagnetic waves traveling along the azimuthally magnetized ferrite-loaded coaxial transmission line and the ferrite-loaded wire. The modal dispersion curves are used to determine the pass and stop bands of normal propagation. Boundary-value problems were solved with Bolle-Heller functions. The dispersion characteristics of transverse electric modes are presented as plots of the normalized propagation constant vs the normalized frequency.

Mueller, R. S.↗
NASA NTRS1960

Criteria for Yielding of Dispersion-Strengthened Alloys

A dislocation model is presented in order to account for the yield behavior of alloys with a finely dispersed second-phase. The criteria for yielding used in the model, is that appreciable yielding occurs in these alloys when the shear stress due to piled-up groups of dislocations is sufficient to fracture or plastically deform the dispersed second-phase particles, relieving the back stress on the dislocation sources. Equations derived on the basis of this model, predict that the yield stress of the alloys varies as the reciprocal square root of the mean free path between dispersed particles. Experimental data is presented for several SAP-Type alloys, precipitation-hardened alloys and steels which are in good agreement with the yield strength variation as a function of dispersion spacing predicted by this theoretical treatment.

Ansell, G. S.↗
NASA NTRS1984

Magnetic field line reconnection experiments. VI - Magnetic turbulence

Extensive statistical analysis of the vector components of fluctuating magnetic fields have been performed in a time dependent neutral magnetic sheet. Cross spectral analysis indicates a variety of wave numbers present for each frequency investigated. Comparison of Fourier components of the cross spectral function with dispersion surfaces in k space demonstrates the waves are large amplitude whistlers; this is verified by polarization analysis, which shows the random waves' magnetic fields to be right-hand circular. Ion acoustic and Langmuir turbulence are also observed along with bursts of microwave radiation. Measurements of the electron distribution function f(v, r, t) and its fluctuations in velocity space relate wave and particle activity.

Gekelman, W.↗