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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Comparisions of modeled N(+), O(+), H(+) and He(+) in the midlatitude ionospherewith mean densities and temperatures from Atmosphere Explorer

In this study, Atmosphere Explorer data and model results for the ion and electron temperature and the density of N(+), O(+), H(+), and He(+) between 120 and 1400 km altitude are compared for two midlatitude ranges (L=2 and L=4), noon and midnight local time, winter and summer, at solar minimum. The data for the heavy atomic ions (O(+) and N(+)) show that their densities are greater at noon than at midnight for a given season and greater in summer than winter for a given local time. There is only a weak latitudinal variation in the density of these ions. The data show that the light ion (H(+) and He(+)) densities are greater at midnight than at noon and are generally greater in winter than summer. There is a strong latitudinal variation of the light ion densities, with the densities decreasing with increasing latitude. The model densities are in good agreement with the AE densities for N(+), O(+), and H(+). Model He(+) densities are lower, by a factor of 2 or more, than the measured densities. Model ion and electron temperatures agree well with the measured temperatures with only a modest increase in plasmapheric heating.

Craven, P. D.↗
NASA NTRS1998

Dynamic Density: An Air Traffic Management Metric

The definition of a metric of air traffic controller workload based on air traffic characteristics is essential to the development of both air traffic management automation and air traffic procedures. Dynamic density is a proposed concept for a metric that includes both traffic density (a count of aircraft in a volume of airspace) and traffic complexity (a measure of the complexity of the air traffic in a volume of airspace). It was hypothesized that a metric that includes terms that capture air traffic complexity will be a better measure of air traffic controller workload than current measures based only on traffic density. A weighted linear dynamic density function was developed and validated operationally. The proposed dynamic density function includes a traffic density term and eight traffic complexity terms. A unit-weighted dynamic density function was able to account for an average of 22% of the variance in observed controller activity not accounted for by traffic density alone. A comparative analysis of unit weights, subjective weights, and regression weights for the terms in the dynamic density equation was conducted. The best predictor of controller activity was the dynamic density equation with regression-weighted complexity terms.

Laudeman, I. V.↗
NASA NTRS2001

Electron Densities Near Io from Galileo Plasma Wave Observations

This paper presents an overview of electron densities obtained near Io from the Galileo plasma wave instrument during the first four flybys of Io. These flybys were Io, which was a downstream wake pass that occurred on December 7, 1995; I24, which was an upstream pass that occurred on October 11, 1999; I25, which was a south polar pass that occurred on November 26, 1999; and I27, which was an upstream pass that occurred on February 22, 2000. Two methods were used to measure the electron density. The first was based on the frequency of upper hybrid resonance emissions, and the second was based on the low-frequency cutoff of electromagnetic radiation at the electron plasma frequency. For three of the flybys, Io, I25, and I27, large density enhancements were observed near the closest approach to Io. The peak electron densities ranged from 2.1 to 6.8 x 10(exp 4) per cubic centimeters. These densities are consistent with previous radio occultation measurements of Io's ionosphere. No density enhancement was observed during the I24 flyby, most likely because the spacecraft trajectory passed too far upstream to penetrate Io's ionosphere. During two of the flybys, I25 and I27, abrupt step-like changes were observed at the outer boundaries of the region of enhanced electron density. Comparisons with magnetic field models and energetic particle measurements show that the abrupt density steps occur as the spacecraft penetrated the boundary of the Io flux tube, with the region of high plasma density on the inside of the flux tube. Most likely the enhanced electron density within the Io flux tube is associated with magnetic field lines that are frozen to Io by the high conductivity of Io's atmosphere, thereby enhancing the escape of plasma along the magnetic field lines that pass through Io's ionosphere.

Gurnett, D. A.↗
NASA NTRS2004

Buoyancy Effects on Flow Structure and Instability of Low-Density Gas Jets

A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. The primary objective of the proposed research is to study buoyancy effects on the origin and nature of the flow instability and structure in the near-field of low-density gas jets. Quantitative rainbow schlieren deflectometry, Computational fluid dynamics (CFD) and Linear stability analysis were the techniques employed to scale the buoyancy effects. The formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and RMS concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. The laminar, axisymmetric, unsteady jet flow of helium injected into air was simulated using CFD. Global oscillations were observed in the flow field. The computed oscillation frequency agreed qualitatively with the experimentally measured frequency. Contours of helium concentration, vorticity and velocity provided information about the evolution and propagation of vortices in the oscillating flow field. Buoyancy effects on the instability mode were evaluated by rainbow schlieren flow visualization and concentration measurements in the near-field of self-excited helium jets undergoing gravitational change in the microgravity environment of 2.2s drop tower at NASA John H. Glenn Research Center. The jet Reynolds number was varied from 200 to 1500 and jet Richardson number was varied from 0.72 to 0.002. Power spectra plots generated from Fast Fourier Transform (FFT) analysis of angular deflection data acquired at a temporal resolution of 1000Hz reveal substantial damping of the oscillation amplitude in microgravity at low Richardson numbers (~0.002). Quantitative concentration data in the form of spatial and temporal evolutions of the instability data in Earth gravity and microgravity reveal significant variations in the jet flow structure upon removal of buoyancy forces. Radial variation of the frequency spectra and time traces of helium concentration revealed the importance of gravitational effects in the jet shear layer region. Linear temporal and spatio-temporal stability analyses of a low-density round gas jet injected into a high-density ambient gas were performed by assuming hyper-tan mean velocity and density profiles. The flow was assumed to be non parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results were delineated. A decrease in the density ratio (ratio of the density of the jet to the density of the ambient gas) resulted in an increase in the temporal amplification rate of the disturbances. The temporal growth rate of the disturbances increased as the Froude number was reduced. The spatio-temporal analysis performed to determine the absolute instability characteristics of the jet yield positive absolute temporal growth rates at all Fr and different axial locations. As buoyancy was removed (Fr . 8), the previously existing absolute instability disappeared at all locations establhing buoyancy as the primary instability mechanism in self-excited low-density jets.

Pasumarthi, Kasyap Sriramachandra↗
NASA NTRS2009

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Johnson, W. L.↗
NASA NTRS2017

Small-Scale Density Variations in the Lunar Crust Revealed by GRAIL

Data from the Gravity Recovery and Interior Laboratory (GRAIL) mission have revealed that approximately 98 percent of the power of the gravity signal of the Moon at high spherical harmonic degrees correlates with the topography. The remaining 2 percent of the signal, which cannot be explained by topography, contains information about density variations within the crust. These high-degree Bouguer gravity anomalies are likely caused by small-scale (10's of km) shallow density variations. Here we use gravity inversions to model the small-scale three-dimensional variations in the density of the lunar crust. Inversion results from three non-descript areas yield shallow density variations in the range of 100-200 kg/m3. Three end-member scenarios of variations in porosity, intrusions into the crust, and variations in bulk crustal composition were tested as possible sources of the density variations. We find that the density anomalies can be caused entirely by changes in porosity. Characteristics of density anomalies in the South Pole-Aitken basin also support porosity as a primary source of these variations. Mafic intrusions into the crust could explain many, but not all of the anomalies. Additionally, variations in crustal composition revealed by spectral data could only explain a small fraction of the density anomalies. Nevertheless, all three sources of density variations likely contribute. Collectively, results from this study of GRAIL gravity data, combined with other studies of remote sensing data and lunar samples, show that the lunar crust exhibits variations in density by plus or minus 10 percent over scales ranging from centimeters to 100’s of kilometers.

J C Jansen↗
DOE OSTI2025

Disentangling core and edge mechanisms of the density limit in DIII-D negative triangularity plasmas

The density limit is investigated in the DIII-D negative triangularity plasmas which lack a standard H-mode edge. We find the limit may not be a singular disruptive boundary but a multifaceted density saturation phenomenon governed by distinct core and edge transport mechanisms. Sustained, non-disruptive operation is achieved at densities up to 1.8 times the Greenwald limit ($n_\mathrm{G}$) until the termination of auxiliary heating. Systematic power scans show distinct power scalings for the core ($n_e \propto P_\mathrm{SOL}^{0.27\pm0.03}$) and edge ($n_e \propto P_\mathrm{SOL}^{0.42\pm0.04}$) density limits. The edge density saturation is triggered by the onset of a non-disruptive, high-field side radiation front and the associated cooling, which clamps the edge density below . In contrast, the core density continues to rise until it saturates, a state characterized by enhanced core turbulence. Core transport evolves from a diffusive to an intermittent, avalanche-like state, as indicated by heavy-tailed probability density functions (kurtosis ≈ 6), increased Hurst exponents, and a $1/f$-type power spectrum. These findings suggest that the density limit in the low-confinement regime is determined by a combination of edge radiative cooling and core turbulent transport. This distinction provides separate targets for control strategies aimed at extending the operational space of future fusion devices.

density limit↗
NASA NTRS1979

Tables of thermospheric temperature, density and composition derived from satellite and ground based measurements. Volume 1: Ap=4

The tables contain the neutral temperature, neutral densities for N2, O2, O, Ar, He and H, mean molecular weight, and total mass density as predicted by the Mass Spectrometer and Incoherent Scatter empirical thermosphere model for selected altitudes, latitudes, local times, days and other geophysical conditions. The model is based on a least squares fit to density data from mass spectrometers on five satellites and temperature data from four incoherent scatter stations, providing coverage for most of solar sunspot cycle 20. Included in the model data base are longitudinally average N3, He, and O densities from the OGO-6 mass spectrometer longitudinally average N2, He, O and Ar densities from the AEROS-A (NATE) mass spectrometer the N2, He, O, and Ar densities from the San Marco 3 mass spectrometer the N2 densities from the AE-B mass spectrometer and the N2, He, O, and Ar densities from the AE-C (OSS, NACE, NATE) mass spectrometers. The O2 and H densities are inferred using ion mass spectrometer data from AE-C (BIMS). Neutral exospheric temperature data are included from Arecibo, St. Santin, Millstone Hill and Jicamarca.

Hedin, A. E.↗
NASA NTRS1986

Size-density relations in dark clouds: Non-LTE effects

One of the major goals of molecular astronomy has been to understand the physics and dynamics of dense interstellar clouds. Because the interpretation of observations of giant molecular clouds is complicated by their very complex structure and the dynamical effects of star formation, a number of studies have concentrated on dark clouds. Leung, Kutner and Mead (1982) (hereafter LKM) and Myers (1983), in studies of CO and NH3 emission, concluded that dark clouds exhibit significant correlations between linewidth and cloud radius of the form delta v varies as R(0.5) and between mean density and radius of the form n varies as R(-1), as originally suggested by Larson (1981). This result suggests that these objects are in virial equilibrium. However, the mean densities inferred from the CO data of LKM are based on an local thermodynamic equilibrium (LTE) analysis of their 13CO data. At the very low mean densities inferred by LKM for the larger clouds in their samples, the assumption of LTE becomes very questionable. As most of the range in R in the density-size correlation comes from the clouds observed in CO, it seems worthwhile to examine how non-LTE effects will influence the derived densities. One way to assess the validity of LTE-derived densities is to construct cloud models and then to interpret them in the same way as the observed data. Microturbulent models of inhomogeneous clouds of varying central concentration with the linewidth-size and mean density-size relations found by Myers show sub-thermal excitation of the 13CO line in the larger clouds, with the result that LTE analysis considerbly underestimates the actual column density. A more general approach which doesn't require detailed modeling of the clouds is to consider whether the observed T sub R*(13CO)/T sub R*(12CO) ratios in the clouds studied by LKM are in the range where the LTE-derived optical depths (and hence column densities) can be seriously in error due to sub-thermal excitation of the 13CO molecule.

Maloney, P.↗
NASA NTRS1988

Electron density distributions in the high-latitude magnetosphere

Electron density profiles were constructed to study the plasma density depletions in the nightside auroral zone and the density variations with increasing altitude in the polar cap, using electric field spectrum measurements from the plasma wave instrument on DE-1. Sharply defined regions of depleted plasma densities were commonly observed on nightside auroral field lines, in which electron densities were strongly depleted in relation to the adjacent plasmaspheric and polar densities, forming a low-density cavity at about 70 deg invariant latitude. A correlation was found between low auroral plasma densities, upflowing ion distributions, and an energetic precipitating electron population, indicating that electron density depletions in the nightside auroral zone are directly associated with auroral acceleration processes.

Persoon, Ann M.↗
NASA NTRS1990

Gravitational star formation thresholds and gas density in three galaxies

It has long been held that the star formation rate (SFR) may be described as a power law of the gas density, p(exp n), as given by Schmidt (1959). However, this relation has as yet remained poorly defined and is likewise poorly understood. In particular, most studies have been investigations of global gas and star formation properties of galaxies, due to lack of adequate high-resolution data for detailed studies of individual galaxies. The three spiral galaxies in this study have published maps of both H2 (as traced by CO), and HI, thereby enabling the authors to investigate the relationship between total gas surface density and SFR. The purpose of the present investigation is the comparison of spatially-resolved total surface gas density in three galaxies (NGC 6946, M51, and M83) to sigma sub c as given by the above model. CO, HI and H alpha data for NGC 6946 were taken from Tacconi-Garman (1988), and for M51 and M83 from Lord (1987). The authors used a CO-H2 conversion of N(H2)/I sub CO(exp cos i = 2.8 x 10(exp 20) atoms cm(-2)/(K kms(-1), and summed the H2 and HI data for each galaxy to obtain the total hydrogen gas density. This total was then multiplied by a factor of 1.36 to include the contribution of helium to the total surface gas density. The authors assumed distances to NGC 6946, M51, and M83 to be 6.0, 9.6, and 8.9 Mpc respectively, with inclination angles of 30, 20, and 26 degrees. H alpha flux was used as the measure of SFR for NGC 6946, and SFR for the remaining two galaxies was taken directly from Lord as computed from H alpha measurements. The results of these full-disk studies thus show a remarkable correlation between the total gas density and the threshold densities given by the gravitational stability criterion. In particular, the threshold density appears to mark a lower boundary to the range of gas densities in these galaxies, which may have consequence in determining appropriate models for star formation and gas dynamics. More evidence is required to verify this result, and the authors are currently undertaking a high-resolution study of the nearby spiral M33 and other galaxies to further investigate this problem.

Oey, M. S.↗
NASA NTRS1992

The density minimum at the earth's magnetic equator

Observations of the density structure in the plasmapause region reveal the existence of a local minimum in the total electron density at the magnetic equator. Data from the plasma wave instrument and ion mass spectrometer on the DE-1 satellite are used to study this phenomenon. The density depletion typically extends from +/- 5 to +/- 20 deg in latitude and is found at altitudes from 2 to 5 RE. Density depletions of 10-70 percent are found in regions where the off-equator density ranges from 10 to 1000/cu cm. This density structure is associated with equator crossings where the thermal plasma has been heated over normal plasmasphere values. The heated plasma is the equatorially trapped plasma previously reported from DE 1 and the SCATHA satellite. Within the plasmasphere, the drop in total (electron) density corresponds to a decrease in the cold-ion density, in both H(+) and He(+). There is a rough pressure balance provided by the warm tail of the distribution, which is a few percent by density but 1-2 orders of magnitude higher in temperature.

Olsen, R. C.↗
NASA NTRS1994

CS multitransitional study of density distribution in star-forming regions. 2: The S140 region

The S140 molecular cloud was observed in five transitions of CS with resolutions of 11 to 45 arcsec. The data were analyzed with both the LVG and microturbulent models of radiative transfer to derive the density structure. It was found that the CS emission comes from three components of gas: a spherical component centered on the infrared cluster, an arc component along the ionization front between the S140 H II region and the dense molecular cloud core, and a high-velocity component from the dense part of a molecular outflow. The spherical component contributes most to the CS emission and was analyzed in more detail than the other components. Using a temperature distribution derived from an analysis of the dust emission from S140, we fit a power-law density distribution of n(r) = n(sub i)(r/r(sub i))(exp -alpha) to the spherical component. The best fit was for n(sub i) = 1.4 x 10(exp 6) (density at r(sub i) = 0.026 pc) and alpha = 0.8. The density (n(sub i)) was found to be greater than or equal to the density required to account for the dust emission, depending on the dust opacity laws adopted. The presence of optical emission (Dinerstein, Lester, & Rank 1979) suggests a clumpy structure for the dense gas. Considerations of the virial mass and the lowest amount of column density required to produce dust emission put the volume filling factor (f(sub nu)) of the dense gas at approximately 0.14-0.5. We compared S140 with other regions of star formation where the density structure has been derived from excitation analysis. Source-source variations in density gradients and clumpiness clearly exist, ranging from alpha = 2 and f(sub nu) approximately 1 in B335 to alpha approximately 0, f(sub nu) approximately 0.1 in M17. There is a tendency for more massive star-forming regions to have a flatter density distribution, a more clumpy structure, and a large number of young stars. The implications of this tendency are discussed.

Zhou, Shudong↗
NASA NTRS1995

What is the source of observed annual variations in plasmaspheric density?

Plasmaspheric densities have been observed previously to be higher in December than in June, with the ratio varying between 1.5 and 3.0 and with larger variations at lower L shells. In order to search for the cause of the observed annual variations, we have modeled plasmaspheric density, using a time-dependent hydrodynamic model. On an L = 2 field line with geomagnetic longitude equal to 300 deg, the modeled plasmaspheric densities were a factor of 1.5 times higher in December than in June. The modeled December to June density ratio was found to increase slightly with L shell, in contrast to observations; this discrepancy may be due to the fact that outer plasmaspheric flux tubes are never completely full. In addition, for an L = 2 field line with geomagnetic longitude equal to 120 deg, the modeled plasmaspheric density was higher in June than in December by a factor of about 1.2. Various numerical tests were also performed in order to examine the sensitivity of plasmaspheric density to various parameters. In particular, a large vertical neutral wind was applied in order to raise the O(+) profile which had the effect of raising plasmaspheric density by a factor of 6. This in conjunction with a theoretical analysis suggests that plasmaspheric density levels are very sensitive to O(+) levels in the upper ionosphere. We conclude that annual variations in plasmaspheric density are due to similar variations in ionospheric O(+).

Guiter, S. M.↗
NASA NTRS1997

Electron density distribution in the magnetosphere

Eight months of differential potential measurements from the POLAR satellite were used to study the electron density distribution in the magnetosphere and its dependence on the level of geomagnetic activity identified by the Kp index. The differential potential measurement is directly proportional to the electron density, and this technique can be used for detecting fast electron density variation in low-density plasmas with a good accuracy. The inner magnetospheric regions are particularly investigated in this study. The cusp is found to be denser during low Km, and it moves equator-ward with increasing Km. The plasmapause is quite asymmetric, as expected. In particular, on the nightside, the plasmapause is compressed closer to the earth with increasing Kp. While the density gradients at the dayside plasmapause are usually not very steep, they can be quite large at other time sectors. A particularly pronounced sharpening of the plasmapause occurs at the dusk sector with increasing Kp. The density in the region between the dayside plasmapause and magnetopause is relatively high during all Kp levels; the average densities are several electrons per cubic meter. During disturbed periods, the density in the near-earth plasma sheet near midnight increases and becomes higher than the densities towards the flanks of the plasma sheet.

Laakso, H.↗
NASA NTRS2000

IMAGE EUV Observations and Modeling of the Plasmaspheric Density Trough Associated with the 24 May 2000 Geomagnetic Storm

The IMAGE EUV imager observed a plasmaspheric density trough in association with a geomagnetically active period on 24 May 2000. At EUV wavelengths, this density trough appeared as an Archimedes spiral extending from Earth's shadow to approximately 1800 MLT. We present an analysis of this density trough using simulated EUV images. Observational EUV images are subjected to edge analysis to establish the plasmapause L-shell and the location of the density trough in terms of L-shell, MLT extent, and radial width. The plasmaspheric density distribution is modeled using both static and dynamic models for the plasmasphere. The background plasmasphere is then numerically simulated using the 4-parameter plasmaspheric density model contained within the Global Core Plasma Model (GCPM) [Gallagher et al., 20001 and the Dynamic Global Core Plasma Model (DGCPM). Simulated EUV images of the model plasmasphere are produced once an artificial density depletion, matching the observed MLT extent and width, has been removed. Once the azimuthal extent and width of the trough have been simulated, the depth of the artificial density depletion is iteratively adjusted to produce simulated EUV images that approximate observation. The results of this analysis and discussion of possible origins for this density trough will be presented.

Adrian, M.L.↗
NASA NTRS2001

The Large-Scale Plasmaspheric Density Trough Associated With the 24 May 2000 Geomagnetic Storm: IMAGE EUV Observations and Global Core Plasma Modeling

The IMAGE EUV imager observed a plasmaspheric density, trough in association with a geomagnetically active period on 24 May 2000. In EUV, this density, trough appears as an Archimedes spiral extending from Earth's shadow to approximately 1900 MLT. We present an analysis of this density trough using simulated EUV images, Observational EUV images are subjected to edge analysis to establish the plasmapause L-shell and the location of the density trough in terms of L-shell, MLT extent, and radial width. The plasmaspheric density distribution is modeled using both static and dynamic models for the plasmasphere. The background plasmasphere is then numerically simulated using the 4-parameter plasmaspheric density model contained within the Global Core Plasma Model (GCPM) and the Dynamic Global Core Plasma Model (DGCPM). Simulated EUV images of the model plasmasphere are produced once an artificial density, depletion, matching the observed MLT extent and width, has been removed. Once the azimuthal extent and width of the trough have been simulated, the depth of the artificial density depletion is iteratively adjusted to produce simulated EUV images that approximate observation. The results of this analysis and discussion of possible origins for this density trough will be presented.

Adrian, M. L.↗
NASA NTRS2012

The Transport of Density Fluctuations Throughout the Heliosphere

The solar wind is recognized as a turbulent magnetofluid, for which the properties of the turbulent velocity and magnetic field fluctuations are often described by the equations of incompressible magnetohydrodynamics (MHD). However, low-frequency density turbulence is also ubiquitous. On the basis of a nearly incompressible formulation of MHD in the expanding inhomogeneous solar wind, we derive the transport equation for the variance of the density fluctuations (Rho(exp 2)). The transport equation shows that density fluctuations behave as a passive scalar in the supersonic solar wind. In the absence of sources of density turbulence, such as within 1AU, the variance (Rho(exp 2)) approximates r(exp -4). In the outer heliosphere beyond 1 AU, the shear between fast and slow streams, the propagation of shocks, and the creation of interstellar pickup ions all act as sources of density turbulence. The model density fluctuation variance evolves with heliocentric distance within approximately 300 AU as (Rho(exp 2)) approximates r(exp -3.3) after which it flattens and then slowly increases. This is precisely the radial profile for the density fluctuation variance observed by Voyager 2. Using a different analysis technique, we confirm the radial profile for Rho(exp 2) of Bellamy, Cairns, & Smith using Voyager 2 data. We conclude that a passive scalar description for density fluctuations in the supersonic solar wind can explain the density fluctuation variance observed in both the inner and the outer heliosphere.

Zank, G. P.↗