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NASA NTRS1981

Environmental effects and large space systems

When planning large scale operations in space, environmental impact must be considered in addition to radiation, spacecraft charging, contamination, high power and size. Pollution of the atmosphere and space is caused by rocket effluents and by photoelectrons generated by sunlight falling on satellite surfaces even light pollution may result (the SPS may reflect so much light as to be a nuisance to astronomers). Large (100 Km 2) structures also will absorb the high energy particles that impinge on them. Altogether, these effects may drastically alter the Earth's magnetosphere. It is not clear if these alterations will in any way affect the Earth's surface climate. Large structures will also generate large plasma wakes and waves which may cause interference with communications to the vehicle. A high energy, microwave beam from the SPS will cause ionospheric turbulence, affecting UHF and VHF communications. Although none of these effects may ultimately prove critical, they must be considered in the design of large structures.

Garrett, H. B.↗
NASA NTRSDate not supplied

Modeling Methods for 3D Lightning Mapping from Space

Global lightning detection has advanced greatly over the past few decades both on ground and from orbit. Ground-based systems like the Lightning Mapping Array (LMA) excel at high-precision 3D reconstruction of local flashes, while spaceborne lightning sensors have much larger potential coverage but are limited by coarser resolution and often rely on data from other instruments to determine 3D flash locations. CubeSpark is a new mission concept focused on combining these two methods in the form of six small satellites in low-Earth orbit. CubeSpark will combine RF and bispectral optical measurements of lightning in order to map the 3D structure of both individual flashes and their parent thunderstorms at 1-2 km spatial resolution on a global scale, enabling a host of new atmospheric, climate, and space electricity studies. The goal of this study is to assess the feasibility and expected resolution of lightning mapping via indivudal VHF sources using different methods and detector combinations. Flashes were simulated beneath orbital configurations consisting of 1-6 satellites, taking into account the complicated interactions with Earth's ionosphere. In the multi-satellite (>5) approach, RF detectors on each satellite measure the arrival times of impulsive VHF sources to collectively pinpoint their locations in 3D and reconstruct flashes with higher resolution than has been achieved from space. The same can process can be performed with 3-4 satellites by constraining sources' horizontal locations with onboard optical imagers. A 1-2 station approach follows the established method of determining the height of an RF source using the arrival time difference between direct RF waves and their reflections off the Earth's surface. Here we present preliminary results of the expected accuracy of these methods to inform potential satellite missions like CubeSpark.

Lightning↗
NASA NTRS1991

Interpretation of Voyager UVS observations of occultations by the atmosphere of Neptune

We propose to continue our investigation of the upper atmosphere of Neptune based primarily on the solar occultation measurements made by the Voyager Ultraviolet Spectrometer (UVS). The ultimate goal of this research is to understand the structure and composition of Neptune's upper atmosphere as encoded in the data base obtained by the UVS during the Voyager 2 encounter with Neptune. The UVS occultations provide information essential to studies of atmospheric composition and structure, energy balance, photochemistry, global transport, ionospheric structure, and airglow production mechanisms. In conjunction with other research in progress at the University of Arizona and by our colleagues at other institutions, we not only analyze and interpret individual measurements or observations by the UVS, but also construct models of the upper atmosphere which are consistent with all available data obtained by the UVS. We derive constraints from measurements of the atmospheric emissions and we combine these with constraints derived from the occultation measurements. Principal sources for the atmospheric emissions include dayglow, resonance scattering and, at long wavelengths, the reflected solar spectrum. On the dark side of the planet, a weak H Ly alpha emission is due to resonance scattering of the sky background and perhaps another source. Thus a wide range of physical processes are at work, and each provides its own constraints on the atmosphere.

Sandel, Bill R.↗
NASA NTRS1997

Global MHD Magnetospheric Simulation of January 10, 1997 Encounter with Magnetic Cloud

We present a global MHD magnetospheric simulation of the encounter of the magnetic cloud with the terrestrial magnetosphere on January 10-11, 1997. The MHD simulation is driven by IMF and solar wind plasma measurements provided by Wind situated about 100 $R_E$ upstream from Earth. Field-aligned currents produced in the model are mapped down to the ionosphere and are directly compared to auroral images from the Polar UVI. Particular attention will be paid to the interval following the the initial shock wave arrival (around 0100 UT on the 1Oth) but preceding the passage of the magnetic cloud proper (commencing at about 0430 UT) for which there was continuous viewing of the entire auroral oval from apogee by Polar. This turbulent period is characterized by numerous dynamic pressure rises and dips and several northward and southward turnings of the IMF, all of which generate dynamic activity in the simulation that is reflected in the mapped field-aligned current patterns. As discussed by Brittnacher et al. in this session, the auroral morphology imaged by UVI during this period includes: shock wave-induced brightening of the oval followed by a pseudo-onset near midnight, several sun-aligned and curled arcs within the polar cap, an expanding polar cap cleared of arcs, and finally substorm onset at 0337 UT. These features will be directly compared to region 1 and 2 current systems as well as cusp currents in the simulation. Spacecraft magnetopause crossings are also predicted by the global simulation and will be compared to observed crossings, including numerous dayside crossings by Geotail on the 1Oth, and geosynchronous crossings early on January 11.

Elsen, R.↗
NASA NTRS1997

Observations of Reflected Ions and Plasma Turbulence for Satellite Potentials Greater Than the Ion Ram Energy

During the TSS-1R mission, the behavior of the ions flowing from the forward hemisphere of the Tethered Satellite System (TSS) satellite was examined as the potential on the satellite was changed from below to above 5 Volts. The ram energy of the ambient atomic oxygen ions is about 5 eV. For satellite potentials less than 5 V, no ions were observed on the ram side of the satellite. When the satellite potential was raised above 5 V, ions were observed to be flowing from the forward region of the satellite. In the region sampled, the ion flux was a few percent of the ambient with energies of about 5 eV. The temperature of the outflowing ions was observed to be enhanced, relative to the ambient ionosphere, and had a maximum in a plane containing the center of the satellite and normal to the geomagnetic field. The net current to the probe package became much more noisy for satellite potentials above 5 V as compared with satellite potentials below 5 V indicating a more disturbed plasma environment.

Wright, K. H., Jr.↗
NASA NTRS1984

Radar echoes at 2.66 and 40.92 MHz from the mesosphere, part 2.6A

During recent decades, the ionospheric D region has been scanned extensively by radar in the frequency range from 1 to 60 MHz. Progress has been made in understanding the reflection/scattering of radio waves in that area. Rocket measurement of ion density irregularities were compared to radar echo observations at 2.75 MHz with the conclusion that the received radar signal was due to scattering from isotropic and homogeneous turbulence in the altitude region between 70 and 95 km. However, scattering cross sections at 2 and 6 mHz suggest that the radar echo from the region below 80 km is in part due to partial reflection from stratified layers. The VHF scattering cross section is aspect sensitive in the D region below about 75 km and tends to be isotropic at higher altitudes. Positive correlations between scattered signal power and signal correlation time (P/C) have been observed by VHF radars in the lower mesosphere, with the conclusion that it might be an additional indication of partial reflection from stratified layers. In the upper mesosphere where the P/C correlation is negative, it is generally believed that the scattering is caused by isotropic turbulence. Radar echoes at the 2.16 and 40.92 MHz ranges are compared, assuming that both result from turbulent scatter. Adjusting the radar Bragg wavelength, it was found that both sets are due to scattering from the same layer of turbulence-generated irregularities.

Royrvik, O.↗
NASA NTRS1998

Observations of Reflected Ions and Plasma Turbulence for Satellite Potentials Greater than the Ion Ram Energy

During the TSS-1R mission, the behavior of the ions flowing from the forward hemisphere of the Tethered Satellite System (TSS) satellite was examined as the potential of the satellite was changed from below to above 5 V. The ram energy of the ambient atomic oxygen ions is approximately 5 eV. For satellite potentials less than 5 V, no ions were observed on the ram side of the satellite. When the satellite potential was raised greater than 5 V, ions were observed to be flowing from the forward region of the satellite. In the region sampled, the ion flux was a few percent of the ambient with energies of approximately 5 eV. The temperature of the out-flowing ions was observed to be enhanced, relative to the ambient ionosphere. The net current to the probe package became much more noisy for satellite potentials greater than 5 V as compared with satellite potentials less than 5 V, indicating a more disturbed plasma environment.

Wright, K. H., Jr.↗
NASA NTRS1992

Monochromatic imaging instrumentation for applications in aeronomy of the earth and planets

Monochromatic imaging instrumentation has been developed that uses narrow-band (12 A FWHP) interference filters or plane reflection gratings for 2D imaging and imaging spectrograph applications. By changing the optics in front of the filter or grating, the field of view of the instruments can be varied from 180 deg to 6 deg. In the case of the 2D monochromatic imager, the 12 mm-diameter filtered image is formed at about f/1 on the input photocathode of an intensified CCD camera (380 x 488 pixels). The sensitivities of the systems are about 50-100 R s (S/N about 2). Examples of data taken with both of these instruments include detection and mapping of Jupiter's sodium magnetonebula and stable auroral red arcs in the terrestrial ionosphere.

Baumgardner, Jeffrey↗
NASA NTRS1994

Temperature minima in the average thermal structure of the middle mesosphere (70 - 80 km) from analysis of 40- to 92-km SME global temperature profiles

Global temperatures have been derived for the upper stratosphere and mesosphere from analysis of Solar Mesosphere Explorer (SME) limb radiance profiles. The SME temperature represent fixed local time observations at 1400 - 1500 LT, with partial zonal coverage of 3 - 5 longitudes per day over the 1982-1986 period. These new SME temperatures are compared to the COSPAR International Ionosphere Reference Atmosphere 86 (CIRA 86) climatology (Fleming et al., 1990) as well as stratospheric and mesospheric sounder (SAMS); Barnett and Corney, 1984), National Meteorological Center (NMC); (Gelman et al., 1986), and individual lidar and rocket observations. Significant areas of disagreement between the SME and CIRA 86 mesospheric temperatures are 10 K warmer SME temperatures at altitudes above 80 km. The 1981-1982 SAMS temperatures are in much closer agreement with the SME temperatures between 40 and 75 km. Although much of the SME-CIRA 86 disagreement probably stems from the poor vertical resolution of the observations comprising the CIRA 86 modelm, some portion of the differences may reflect 5- to 10-year temporal variations in mesospheric temperatures. The CIRA 86 climatology is based on 1973-1978 measurements. Relatively large (1 K/yr) 5- to 10-year trends in temperatures as functions of longitude, latitude, and altitude have been observed for both the upper stratosphere (Clancy and Rusch, 1989a) and mesosphere (Clancy and Rusch, 1989b; Hauchecorne et al., 1991). The SME temperatures also exhibit enhanced amplitudes for the semiannual oscillation (SAO) of upper mesospheric temperatures at low latitudes, which are not evident in the CIRA 86 climatology. The so-called mesospheric `temperature inversions' at wintertime midlatitudes, which have been observed by ground-based lidar (Hauschecorne et al., 1987) and rocket in situ measurements (Schmidlin, 1976), are shown to be a climatological aspect of the mesosphere, based on the SME observations.

Clancy, R. Todd↗
NASA NTRS1997

Force Balance and Substorm Effects in the Magnetotail

A model of the quiet time middle magnetotail is developed using a consistent orbit tracing technique. The momentum equation is used to calculate geocentric solar magnetospheric components of the particle and electromagnetic forces throughout the current sheet. Ions generate the dominant x and z force components. Electron and ion forces almost cancel in the y direction because the two species drift earthward at comparable speeds. The force viewpoint is applied to a study of some substorm processes. Generation of the rapid flows seen during substorm injection and bursty bulk flow events implies substantial force imbalances. The formation of a substorm diversion loop is one cause of changes in the magnetic field and therefore in the electromagnetic force. It is found that larger forces are produced when the cross-tail current is diverted to the ionosphere than would be produced if the entire tail current system simply decreased. Plasma is accelerated while the forces are unbalanced resulting in field lines within a diversion loop becoming more dipolar. Field lines become more stretched and the plasma sheet becomes thinner outside a diversion loop. Mechanisms that require thin current sheets to produce current disruption then can create additional diversion loops in the newly thinned regions. This process may be important during multiple expansion substorms and in differentiating pseudoexpansions from full substorms. It is found that the tail field model used here can be generated by a variety of particle distribution functions. However, for a given energy distribution the mixture of particle mirror or reflection points is constrained by the consistency requirement. The study of uniqueness also leads to the development of a technique to select guiding center electrons that will produce charge neutrality all along a flux tube containing nonguiding center ions without the imposition of a parallel electric field.

Kaufmann, Richard L.↗
NASA NTRS2013

Analytic Theory of Titans Schumann Resonance: Constraints on Ionospheric Conductivity and Buried Water Ocean

This study presents an approximate model for the atypical Schumann resonance in Titan's atmosphere that accounts for the observations of electromagnetic waves and the measurements of atmospheric conductivity performed with the Huygens Atmospheric Structure and Permittivity, Wave and Altimetry (HASI-PWA) instrumentation during the descent of the Huygens Probe through Titan's atmosphere in January 2005. After many years of thorough analyses of the collected data, several arguments enable us to claim that the Extremely Low Frequency (ELF) wave observed at around 36 Hz displays all the characteristics of the second harmonic of a Schumann resonance. On Earth, this phenomenon is well known to be triggered by lightning activity. Given the lack of evidence of any thunderstorm activity on Titan, we proposed in early works a model based on an alternative powering mechanism involving the electric current sheets induced in Titan's ionosphere by the Saturn's magnetospheric plasma flow. The present study is a further step in improving the initial model and corroborating our preliminary assessments. We first develop an analytic theory of the guided modes that appear to be the most suitable for sustaining Schumann resonances in Titan's atmosphere. We then introduce the characteristics of the Huygens electric field measurements in the equations, in order to constrain the physical parameters of the resonating cavity. The latter is assumed to be made of different structures distributed between an upper boundary, presumably made of a succession of thin ionized layers of stratospheric aerosols spread up to 150 km and a lower quasi-perfect conductive surface hidden beneath the non-conductive ground. The inner reflecting boundary is proposed to be a buried water-ammonia ocean lying at a likely depth of 55-80 km below a dielectric icy crust. Such estimate is found to comply with models suggesting that the internal heat could be transferred upwards by thermal conduction of the crust, while convective processes cannot be ruled out.

TITAN↗
NASA NTRS1973

On Lidar Sounding of the Atmosphere to Estimate Static and Dynamic Characteristics of Aerosol Inhomogeneities

1. A possible application of intensity fluctuations of a pulse light signal reflected by atmospheric aerosols is analyzed by the correlation method to evaluate static (medium sizes, shape) and dynamic (speed and direction of movement, lifetime) characteristics of aerosol inhomogeneities. The aerosol inhomogeneities are assumed to be expanded, pressed, disintegrated and originated constantly in accordance with random laws, the set of inhomogeneities as a whole traveling together with air masses and having predominant movement in wind direction. It is shown that the characteristics of aerosol inhomogeneities considered can be expressed by the coefficients of the correlation function expansion of the reflected signal fluctuation intensity in Tailor series. 2/ Correlation systems for evaluating static and dynamic characteristics of driving objects can be divided into two types according to the kind and quantity of used information: the systems with coordinates of the information removal "points" to be fixed in space, and the systems with a parallel simultaneous information removal at discrete moments of time. The systems for determination of wind direction considered in are the examples of the first type system. However, the operating information removal for two points is insufficient to estimate completely static and dynamic characteristics of inhomogenities, their quantity ought to be increased up to three of them for two-dimensional problem and up to four of them for three-dimensional problem as it is usually done in the ionospheric studies. The second type systems are used for the investigation of a medium shape and speed of the clouds according to photographs made from satellites. These systems are also used for solution of navigation problems. The use of optical quantum generators with a scanning beam is seen to increase greatly the working information removal in comparison with the first type systems. Nevertheless, scanning rate is not sufficient sometimes in order· to consider a general picture of aerosol inhomogeneities to be stationary. In this connection the use of the systems of second type treatment becomes a matter of essential difficulty. 3. Aerosol inhomogeneities simulation has been carried out on the basis of the digital computer experiments with the aim of estimating static and dynamic characteristics of inhomogeneities by an optical beam in the atmosphere at different scanning procedures. The dependence of determination accuracy of these characteristics on the type of chosen laws of aerosol particle distribution in the atmosphere, the parameters of inhomogeneities geometry, their speed and the law of scanning have been obtained.

Zuev, V. E.↗
NASA NTRS1994

Landau damping of magnetospherically reflected whistlers

Unducted VLF signals produced by lightning activity can form a population of magnetospherically reflected (MR) whistlers in the inner magnetosphere. It has been suggested recently that in the absence of significant attenuation such waves could merge into a broadband continuum with sufficient intensity to account for plasmaspheric hiss. To test this conjecture we have evaluated the path-integrated attenuation of MR whistlers along representative ray paths using the HOTRAY code. Using a realistic plasma distribution modeled on in-situ data, we find that the majority of MR waves experience significant damping after a few transits across the equator. This is primarily due to Landau resonance with suprathermal (0.1-1 keV) electrons. The attenuation is most pronounced for waves that propagate through the outer plasmasphere; this can readily account for the infrequent occurrence of multiple-hop MR waves for L greater than or equal to 3.5. Selected waves that originate at intermediate latitudes (15 deg is less than or equal to lambda is less than or equal to 35 deg) and whose ray paths are confined to the inner plasma- sphere may experience up to 10 magnetospheric reflections before substantial attentuation occurs. These waves should form the population of observed MR waves. Wave attenuation becomes more pronounced at higher frequencies; this can account for the absence of multiple-hop waves above 5 kHz. Weakly attenuated MR waves tend to migrate outward to the L shell, where their frequency is comparable to the equatorial lower hybrid frequency. The enhanced concentration of waves due to a merging of ray paths would produce a spectral feature that rises in frequency at lower L. This is quite distinct from the reported properties of plasmaspheric hiss, which maintains a constant frequency band throughout the entire plasmasphere. Furthermore, in the absence of mode conversion, waves below 500 Hz, which often form an important if not dominant part of the spectral properties of hiss, are unable to escape from the topside ionosphere in the whistler mode. Consequently, we conclude that unducted lightning signals cannot account for the origin of plasmaspheric hiss.

Thorne, Richard M.↗
NASA NTRS1994

Substorm recurrence during steady and variable solar wind driving: Evidence for a normal mode in the unloading dynamics of the magnetosphere

Farrugia et al (1993) have recently studied substorm activity driven by the passage of an interplanetary magnetic cloud during which the interplanetary magnetic field turned southward for approximately 18 hours. It was shown that both the epsilon and the VB(sub s) parameters varied slowly on the timescale of a substorm but changed considerably over the interval as a whole. The substorm occurrence rate did not reflect the variation in magnetospheric energy loading rate as measured by these parameters but, rather, remained roughly constant with a 50-min average period. Klimas et al. (1992) showed that the Faraday loop analog model of geomagnetic activity predicts this single unloading rate under various constant loading rates. However, various model parameters were adjusted to yield a 1-hour unloading period in agreement with the Bargatze et al. (1985) linear prediction filters and in approximate agreement with the Farrugia et al. (1993) results. It has since been found necessary to add a slow relaxation mechanism to the Faraday loop model to allow for its approach to a ground state during long periods of inactivity. It is proposed that the relaxation mechanism is provided by slow convection of magnetic flux out of the magnetotail to the dayside magnetosphere. In addition, a rudimentary representation of magnetotail-ionosphere coupling has been added to enable comparison of model output to measured AL. The present study is of the modified Faraday loop model response to solar wind input from the Bargatze et al. data set with comparison of its output to concurrent AL. This study has removed the degree of freedom in parameter choice that had earlier allowed adjustments toward the 1-hour unloading period and has, instead, yielded the 1-hour unloading period under various constant loading rates. It is demonstrated that the second peak of the bimodal Bargatze et al. linear prediction filters at approximately equal 1-hour lag and the approximately constant substorm recurrence rate observed by Farrugia et al. can be interpreted as both being due to the existence of a normal unloading recurrence period in the dynamics of the magnetosphere.

Klimas, A. J.↗
NASA NTRS1981

Ionospheric theory

The effects of the atmospheric dynamics on the ionosphere and neutral chemistry of the stratosphere, mesosphere, and thermosphere were studied. Effects of vertically propagating planetary waves on NO densities in the 70 to 120 km altitude region were investigated. A time dependent model was developed to calculate the transport of NO due to planetary wave induced winds. These transports are sensitive to the planetary wave forcing used at the lower boundary, as well as to the structure of the zonal mean basic state. Fluxes and transport of NO are calculated for the months of January and February, using a separate basic state and boundary forcing for each month. The zonal mean wind profile for the months of January and February were inferred from NMC data. A major stratospheric warming occurred near the end of the month of February. The large planetary wave amplitude and reduction in zonal mean wind velocities due to this warming are reflected in the February average boundary forcing and zonal mean state.

Source record↗
NASA NTRS1994

Hubble Space Telescope UV spectral observations of Io passing into eclipse

Time-resolved spectra of Io have been obtained with the Faint Object Spectrograph on the Hubble Space Telescope in January 1992 at times centered on the passage of Io into Jupiter's shadow. Two different eclipse observations covered 1100-1600 A and 2250-3300 A. In the far ultraviolet(far-UV) range, emission lines of atomic sulfur and oxygen from Io's atmosphere (similar to those previously detected with the International Ultraviolet Explorer (IUE)) have been observed from Io in sunlight, and the spatial extent of the emitting region has been resolved for the first time: this is 0.5-1 Io radii (R(sub Io)) above the surface. The emission lines are typically 1kR in brightness while Io is in sunlight, and decrease to a few hundred Rayleighs within 20 min or less of Io's passing into shadow. If the emissions are produced in Io's ionosphere, the decrease in shadow appears consistent with the collisional slowing and recombination of photoelectrons in 100-1000 s, with recombination an important quenching process if the dominant ion is molecular (i.e., SO2(+)) condensation, with the residual emission in shadow due either to plasma impact of gas above the hot volcanic calderas or electron impact on S and O. In the near-UV range, we have not detected any airglow emissions from Io's atmosphere in shadow, with the main limitation being a high level of scattered light from Jupiter. We derive a 3 sigma upper limit to the 2560 A SO emission feature of 1 KR, which is close to what is expected from electron impact on SO2 based on the obs erved brightness of the FUV S and O lines in shadow. A high signal-to-noise spectrum of Io's albedo in sunlight reveals a spectral shape similar to laboratory spectra of SO2 frost reflectivity, and the relative albedo spectrum changed as Io passed into eclipse and part of the disk was in shadow. No specific SO2 gas absorption features appear in the albedo spectrum, although there could be substantial gas absorption near 2800 A if the individual lines are narrow and saturated. Finally, we present preliminary models for the near-UV spectrum of Io as functions of SO2 frost areal coverage and SO2 gas density.

Clarke, John T.↗
NASA NTRS1972

Measurements of O(1 D) quenching rates in the F-region

In-situ determinations of the quenching of O(1 D) atoms by N2 and O2 molecules were made from observations of 6300 A nightglow intensity enhancements produced by the Platteville 1.6 MW transmitter. The heating of F-region electrons near the point of reflection of the RF wave leads to electron impact excitation of oxygen atoms to the O(1 D) state. It is shown that the resulting region of enhance 6300 A emission is localized to the region of electron energy absorption for heating at the lower altitudes. At 225 km the measured time constants for intensity buildup following transmitter turn-on and for intensity decay following turn-off are identical and equal to (13 plus or minus 1) sec. Time constants varying from 30 to 80 sec are found for the altitude range 260 to 300 km. The inferred quenching coefficient for the whole altitude range, 225 to 300 km, is 4.4 + 2 or - 1 x 10 to the minus 11th power cu cm/sec at 950 K, in good agreement with laboratory data. The quenching frequency obtained at 225 km, when referred to the altitude 120 km, is equal to (21 plus or minus 2)/sec, in agreement with less direct ionospheric determinations.

Sipler, D. P.↗
NASA NTRS1995

Ponderomotive effects on distributions of O(+) ions in the auroral zone

Test particle calculations are used to compute the effects of gravity and ponderomotive acceleration by shear Alfven wave oscillations on the distribution function of O(+) ions along auroral field lines, assuming an ionospheric Maxwellian source of the ions at 2000 km altitude with approximately 0.5 eV of thermal energy in the parallel component of velocity. The electric field model corresponds to a standing wave oscillation with a frequency approximately 1 Hz in the azimuthal direction superimposed on the background dipole field, in which the wave amplitude is either increasing or decreasing in time. The electric field is taken to be primarily in the perpendicular direction. The time varying wave produces broad distributions with widths of 2 to 10 times the initial 0.5-eV thermal energy of the Maxwellian source, and the density and flux of upward going O(+) ions at one Earth radius are both enhanced in this model. The oxygen ion distribution functions at 1 R(sub E) altitude resulting from interaction with waves whose amplitudes are increasing in time have a more gradual lower energy cutoff than do the distribution functions resulting from decaying waves. The high-energy part of the distribution functions in growing waves reflects the temperature of the Maxwellian source, while the high-energy part of the distributions resulting from decaying waves steepens with time, independent of the source temperature.

Witt, E.↗