Auroral ion velocity distributions using a relaxation model

For application to the auroral ionosphere we have calculated ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields. By replacing the Boltzmann collision integral with a simple relaxation model, we have been able to obtain an exact solution to Boltzmann's equation. This solution has the advantage over a series expansion in that all the higher order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, we can determine when the higher order velocity moments affect the ion velocity distribution and the nature of their effect, but we cannot obtain accurate quantitative results. The higher velocity moments have their greatest effect on the distribution function above about 120 km, where the ion-neutral collision frequency is less than the ion cyclotron frequency. As the magnitude of the electric field increases, these higher moments act to decrease the number of ions at the peak of the distribution function. Peak densities are reduced by a few per cent for perpendicular electric fields of about 20 mV m^?1.     

Ion velocity distributions in the auroral ionosphere

For application to studies of the auroral ionosphere we have calculated the velocity distribution of the ions in a weakly-ionized plasma subjected to crossed electric and magnetic fields. We have retained enough terms in the series expansion of the distribution to enable us to determine under what conditions departures from the Maxwellian form become significant and what the nature of these departures is, but we cannot calculate precise values of the distribution function when the departures are large. Departures are negligibly small under conditions appropriate to the auroral ionosphere at low altitudes, where the ion-neutral collision frequency is much larger than the ion cyclotron frequency. At altitudes above about 120 km, however, the magnitude of the departures varies little with altitude. Electric fields greater than 25 mV m⁻¹ cause departures from the Maxwellian distribution that are greater than 20 per cent at random velocities equal to or greater than twice the mean thermal speed of the ions. Under almost all conditions we find that the distribution is depleted in ions moving parallel to the magnetic field relative to those moving perpendicular, an effect that might be detectable in ionospheric measurements of ion temperature.     

Auroral ion velocity distributions for a polarization collision model

We have calculated the effect that convection electric fields have on the velocity distribution of auroral ions at the altitudes where the plasma is weakly-ionized and where the various ion-neutral collision frequencies are much smaller than the ion cyclotron frequencies, i.e. between about 130 and 300 km. The appropriate Boltzmann equation has been solved by expanding the ion velocity distribution function in a generalized orthogonal polynomial series about a bi-Maxwellian weight factor. We have retained enough terms in the series expansion to enable us to obtain reliable quantitative results for electric field strengths as large as 90 mV m^?1. Although we have considered a range of ion-neutral scattering mechanisms, our main emphasis has been devoted to the long-range polarization interaction. In general, we have found that to lowest order the ion velocity distribution is better represented by a two-temperature or bi-Maxwellian distribution than by a one-temperature Maxwellian, with there being different ion temperatures parallel and perpendicular to the geomagnetic field. However, the departures from this zeroth-order bi-Maxwellian distribution become significant when the ion drift velocity approaches (or exceeds) the neutral thermal speed.     

Auroral ion velocity distribution function: The Boltzmann model revisited

The velocity distribution of ion populations is calculated for auroral conditions where strong convection electric fields exist. The Boltzmann equation has been solved for the E and F regions of the ionosphere where plasma is weakly dense, weakly ionized and where the ion-neutral collision frequency is small in regard to the ion cyclotron frequency. The ion distribution function has been expanded in a generalized orthogonal polynomial series about a bi-Maxwellian “temperature” varying weight function. This generalized Grad solution expansion enables us to obtain good approximations for electric field strengths as large as 75 mV m^?1 and 115 mV m^?1 respectively, for both the resonant charge exchange and the polarization collision models. The instability threshold of these distribution functions appears to be higher than the two respective electric field strengths considered above.     

Remarks concerning the diffusion of ion clouds in the earth's upper atmosphere

The diffusive motion of initially ellipsoidal plasma irregularities or ion clouds in the Earth's upper atmosphere is studied theoretically using a model similar to that described by Pickering (1972) for an initially spherical cloud. The work presented here concerns irregularities with major to minor axis ratio between 10:1 and 200:1 at each of the altitudes 97.5 km, 102 km and 114 km (where the ionization could be produced by meteors) and between approximately 200:1 and 1000:1 for altitudes 210 km and 300 km. In particular the effect of the space-charge electric field on the nature of the diffusion process is discussed. The possible effects of ionospheric electric fields and possible relevance to artificial Ba⁺ clouds released in the upper atmosphere are discussed in the second section.     

Observations of outflowing ion beams on auroral field lines at altitudes of many earth radii

The composition, energy and angular characteristics of upward flowing ionospheric ions at altitudes greater than ～ 20,000 km have been studied by means of the PROGNOZ-7 ion composition experiment. Very narrow beams, having widths corresponding to a mirroring altitude of the order a few thousand kilometers or less, may be found up to altitudes exceeding 30,000 km on the nightside. At much higher altitudes and in regions connected to the dayside/flank boundary layer and plasma mantle, the beams are much broader than expected from adiabatic particle motions from an ionospheric source/acceleration region, suggesting that pitch angle scattering or transverse acceleration processes are present there. Considerable mass dispersion effects have also been observed in some upward flowing ionospheric ion beams. The peak energy for the O⁺ ions may differ by several keV compared to that for the H⁺ ions in one and the same ion beam at altitudes above ～ 20,000 km. The O⁺ ions in these beams have gained considerably more energy than H⁺ in the acceleration process. Many examples with a much higher O⁺ than H⁺ content in the beam have been observed. Possible mechanisms giving rise to the observed effects are discussed, one being several kV of potential drop below the neutral H, O-crossover altitude (500–1500 km). At altitudes where the upflowing ionospheric ions are intermixed with magnetosheath ions, mass dispersion effects are also observed. This dispersion often appears to be the result of a velocity filtering effect caused by the dawn-dusk electric field (earthward convection).     

The source of midlatitude metallic ions at F-region altitudes

A survey of metallic ions detected by the Bennett Ion Mass Spectrometers flown on the Atmosphere Explorer satellites, including both circular and eccentric orbital configurations, shows that patches of these ions of meteoric origin are frequently present during magnetically active periods on the bottomside of the F-layer at middle and high latitudes. In particular the F-region metals statistically tend to appear at night in the vicinity of the main ionospheric trough (in a band of invariant latitudes approx. 10 degrees wide) and on the day side of the polar cap. These distributions were previously associated with the expected dynamics of ions in the F-region above 140 km where meridional neutral wind drag and convection electric fields are the dominant ion transport mechanisms. However, the main meteor deposition layer—the presumed source region of the metals—is located below 100 km where these transport mechanisms do not prevail. It is demonstrated that the Pedersen ion drifts driven by intense electric fields such as those associated with sub-auroral ion drifts (SAID) are sufficient to transport the long-lived metallic ions upward from the main meteor layer to altitudes where the drag of equatorial directed neutral winds and electric field convection can support them against the downward pull of gravity and transport them to other locations. The spatial and temporal distribution of the middle and high latitude F-region metals are consistent with the known characteristics of the electric fields and with the expected F-region ion dynamics.     

Comparative study of ion cyclotron waves at Mars, Venus and Earth

Ion cyclotron waves are generated in the solar wind when it picks up freshly ionized planetary exospheric ions. These waves grow from the free energy of the highly anisotropic distribution of fresh pickup ions, and are observed in the spacecraft frame with left-handed polarization and a wave frequency near the ion’s gyrofrequency. At Mars and Venus and in the Earth’s polar cusp, the solar wind directly interacts with the planetary exospheres. Ion cyclotron waves with many similar properties are observed in these diverse plasma environments. The ion cyclotron waves at Mars indicate its hydrogen exosphere to be extensive and asymmetric in the direction of the interplanetary electric field. The production of fast neutrals plays an important role in forming an extended exosphere in the shape and size observed. At Venus, the region of exospheric proton cyclotron wave production may be restricted to the magnetosheath. The waves observed in the solar wind at Venus appear to be largely produced by the solar-wind-Venus interaction, with some waves at higher frequencies formed near the Sun and carried outward by the solar wind to Venus. These waves have some similarity to the expected properties of exospherically produced proton pickup waves but are characterized by magnetic connection to the bow shock or by a lack of correlation with local solar wind properties respectively. Any confusion of solar derived waves with exospherically derived ion pickup waves is not an issue at Mars because the solar-produced waves are generally at much higher frequencies than the local pickup waves and the solar waves should be mostly absorbed when convected to Mars distance as the proton cyclotron frequency in the plasma frame approaches the frequency of the solar-produced waves. In the Earth’s polar cusp, the wave properties of ion cyclotron waves are quite variable. Spatial gradients in the magnetic field may cause this variation as the background field changes between the regions in which the fast neutrals are produced and where they are re-ionized and picked up. While these waves were discovered early in the magnetospheric exploration, their generation was not understood until after we had observed similar waves in the exospheres of Mars and Venus.     

Field-aligned suprathermal electron fluxes below 270 km in the auroral zone

Observations are reported of field aligned etectron fluxes in the energy range 50–500 eV at altitudes below 270 km from two rocket flights in the auroral zone. The regions of field aligned suprathermal electrons occurred in bursts of a few seconds duration, and in some instances the energy of the peak field aligned flux was in the range 100–500 eV. Theoretical calculations of the pitch angle distribution were made using the Monte Carlo technique for two model atmospheres having exospheric temperatures of 750 and 1500 K bracketing the expected auroral zone exospheric temperature. The calculations were made for the case of incident field aligned suprathermal fluxes with no local parallel electric field and also for the case of a local constant parallel electric field. Comparison of theoretical and experimental pitch angle distributions showed that in one case at 270 km a parallel electric field of 1–2 mV/m fitted the data whereas another burst at 210 km required a parallel electric field of about 10 mV/m to produce a field aligned distribution of 230 eV electrons as pronounced as was observed. Furthermore in this latter case the lack of strong field alignment at 500 eV pointed to localisation of the parallel electric field to an altitude range of 20–30 km about the rocket altitude.     

A Monte Carlo Simulation of the H+ Polar Wind: Effect of Velocity Distributions with Kappa Suprathermal Tails

A Monte Carlo simulation is used to study the effects of Kappa H⁺distributions in the polar wind. We consider the gravity, the polarization electric field, the divergence of geomagnetic field lines and Coulomb collisions of H⁺ in a background of O⁺ ions. The aim is to study the consequences of a velocity distribution function with an enhanced high energy tail instead of a Maxwellian distribution as assumed in earlier Monte Carlo simulations. The transformation of the velocity distribution function of H⁺ ions as a function of the altitude is presented. Effects resulting from the acceleration of the particles by the polarization electric field and from Coulomb collisions depend on the energy of the particles. Coulomb collisions mainly affect low energy particles while high energy particles are more efficiently accelerated by the upward directed ambipolar electric field. The combination of both effects results in double-hump velocity distribution functions developing in the transition region. We study consequences of suprathermal tails distributions on the shape of the double-hump and on the moments of the velocity distribution function. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theoretical ion densities in the lower ionosphere

We have solved the coupled momentum and continuity equations for NO⁺, O₂⁺, and O⁺ions in the E- and F-regions of the ionosphere. This theoretical model has enabled us to examine the relative importance of various processes that affect molecular ion densities. We find that transport processes are not important during the day; the molecular ions are in chemical equilibrium at all altitudes. At night, however, both diffusion and vertical drifts induced by winds or electric fields are important in determining molecular ion densities below about 200 km. Molecular ion densities are insensitive to the O⁺ density distribution and so are little affected by decay of the nocturnal F-region or by processes, such as a protonospheric flux, that retard this decay. The O⁺ density profile, on the other hand, is insensitive to molecular ion densities, although the O⁺ diffusion equation is formally coupled to molecular ion densities by the polarization electrostatic field. Nitric oxide plays an important role in determining the NO⁺ to O₂⁺ ratio in the E-region, particularly at night. Nocturnal sources of ionization are required to maintain the E-region through the night. Vertical velocities induced by expansion and contraction of the neutral atmosphere are too small to affect ion densities at any altitude.     

Some aspects of electric field mapping in the auroral ionosphere

The mapping of the spectra of electrostatic field below 300 km altitude is theoretically calculated for a horizontally stratified auroral ionosphere. Perpendicular electric fields of large scale size are the same for different altitudes of the ionosphere. However, electric fields of small scale size vary with altitude and decrease drastically when the scale size is smaller than a certain value which depends on altitude. These results are similar to those observed by satellites above 300 km altitude. In the case of a homogeneous anisotropic ionosphere, analytical results are obtained for the penetration of electric field into the ionosphere as a function of wavenumber. The “smoothing” of the electric field when penetrating a horizontally stratified ionosphere is demonstrated. The smallest possible scale of parallel electric field structure within the ionosphere is found. Also presented is a method of finding the smallest horizontal length with which the electric field can penetrate the ionosphere with little distortion. For an average conductivity model, this length is found to be about 1 km. Finally, the mapping of packets of electric field to the ground is constructed.     

Ionospheric plasma acceleration at Mars: ASPERA-3 results

The Analyzer of Space Plasma and Energetic Atoms (ASPERA) on-board the Mars Express spacecraft (MEX) measured penetrating solar wind plasma and escaping/accelerated ionospheric plasma at very low altitudes (250 km) in the dayside subsolar region. This implies a direct exposure of the martian topside atmosphere to solar wind plasma forcing leading to energization of ionospheric plasma. The ion and electron energization and the ion outflow from Mars is surprisingly similar to that over the magnetized Earth. Narrow “monoenergetic” cold ion beams, ion beams with broad energy distributions, sharply peaked electron energy spectra, and bidirectional streaming electrons are particle features also observed near Mars. Energized martian ionospheric ions (O⁺, O⁺₂, CO⁺₂, etc.) flow in essentially the same direction as the external sheath flow. This suggests that the planetary ion energization couples directly to processes in the magnetosheath/solar wind. On the other hand, the beam-like distribution of the energized plasma implies more indirect energization processes like those near the Earth, i.e., energization in a magnetized environment by waves and/or parallel (to B) electric fields. The general conditions for martian plasma energization are, however, different from those in the Earth's magnetosphere. Mars has a weak intrinsic magnetic field and solar wind plasma may therefore penetrate deep into the dense ionospheric plasma. Local crustal magnetization, discovered by Acuña et al. [Acuña, M.J., Connerey, J., Ness, N., Lin, R., Mitchell, D., Carlsson, C., McFadden, J., Anderson, K., Rème, H., Mazelle, C., Vignes, D., Wasilewski, P., Cloutier, P., 1999. Science 284, 790-793], provide some dayside shielding against the solar wind. On the other hand, multiple magnetic anomalies may also lead to “hot spots” facilitating ionospheric plasma energization. We discuss the ASPERA-3 findings of martian ionospheric ion energization and present evidences for two types of plasma energization processes responsible for the low- and mid-altitude plasma energization near Mars: magnetic field-aligned acceleration by parallel electric fields and plasma energization by low frequency waves.     

Interaction of particles with ion cyclotron waves and magnetosonic waves. Observations from GEOS 1 and GEOS 2

Coordinated observations involving ion composition, thermal plasma, energetic particle, and ULF magnetic field data from GEOS 1 and 2 often reveal the presence of electromagnetic ion cyclotron and magnetosonic waves, which are distinguished by their respective polarization characteristics and frequency spectra. The ion cyclotron waves are identified by a magnetic field perturbation that lies in a plane perpendicular to the Earth's magnetic field B₀ and propagate along B₀. They are associated with the abundance of cold He⁺ in the presence of anisotropic pitch angle distributions of ions having energies E > 20 keV, and were observed at frequencies near the He⁺ gyrofrequency. The magnetosonic waves are characterized by a magnetic field perturbation parallel to B₀ and thus seem to be propagating perpendicular to the Earth's magnetic field. They often occur at harmonics (not always including the fundamental) at the proton gyrofrequency and are associated with phase-space-density distributions that peak at energies E ～ 5–30 keV and at a pitch angle of 90°. Such a ring-like distribution is shown to excite instability in the magnetosonic mode near harmonics of the proton gyrofrequency. Magnetosonic waves are associated in other cases with sharp spatial gradients in energetic ion intensity. Such gradients are encountered in the early afternoon sector (as a consequence of the drift shell distortion caused by the convection electric field) and could likewise constitute a source of free energy for plasma instabilities.     

A numerical hydrodynamic study of coalescence in head-on collisions of identical stars

A two-dimensional hydrodynamic code has been developed for numerical studies of stellar collisions. The motivation for the study has been the suggestion by Colgate that collisions among stars in a dense galactic core can lead to growth of stellar masses by coalescence and thus to an enhanced rate of supernova activity. The specific results reported here refer to head-on collisions between identical polytropes of index 3 having solar mass and radius. If the polytropes were initially at rest at infinity, then about five percent of the combined mass is lost by ejection following collision. The volatilized mass fraction rises to about 18% for an initial relative collision velocity of 1000 km s^–1 at infinite separation, and to about 60% for the 2000 km s^–1 case. Since the initial kinetic and gravitational energies balance for a relative velocity of 1512 km s^–1 at infinity, it may be seen that net coalescence persists to velocities somewhat in excess of this figure. Mass ejection takes place in two ways simultaneously: (1) by a rapid sideward expulsion of fluid in a massive lateral sheet normal to the collision axis, and (2) as a result of two recoil shocks which lead momentum flows backwards along this axis. The lateral effect has similarities to the expansion of gas into a vacuum; that is, shocks are not involved. However, the ejection of material from the rear colliding hemisphere due to the recoil shocks predominates at low collision velocities. As the velocity increases, both effects strengthen, but the lateral expulsion intensifies more rapidly than the recoil shocks.     

Auroral ion velocity distribution function: Generalized polynomial solution of Boltzmann's equation

The ion distribution function is calculated for the E and the F regions of the auroral latitudes. In these regions the plasma is weakly ionized and there exist convective electric fields which may attain very significant intensities. Boltzmann's equation is solved in the limit where the ion-neutral collision frequency is much lower than the ion gyrofrequency. This solution is obtained in the form of a generalized polynomial series expansion starting from a good zeroth-order approximation. With this weight function, and considering a development to the order of the 32 moments, good approximations are obtained for high electric fields. The resonant charge exchange model and the polarization model are successively considered. The Post-Rosenbluth instability threshold is discussed for the above two models.     

Thermal response properties of the Earth's ionospheric plasma

The thermal response of the Earth's ionospheric plasma is calculated for various suddenly applied electron and ion heat sources. The time-dependent coupled electron and ion energy equations are solved by a semi-automatic computational scheme that employs Newton's method for coupled vector systems of non-linear parabolic (second order) partial differential equations in one spatial dimension. First, the electron and composite ion energy equations along a geomagnetic field line are solved with respect to a variety of ionospheric heat sources that include: thermal conduction in the daytime ionosphere; heating by electric fields acting perpendicular to the geomagnetic field line; and heating within a stable auroral red are (SAR-arc). The energy equations are then extended to resolve differential temperature profiles, first for two separate ion species (H⁺, O⁺) and then for four separate ion species (H⁺, He⁺, N⁺, O⁺) in addition to the electron temperature. The electron and individual ion temperatures are calculated for conditions within a night-time SAR-arc excited by heat flowing from the magnetosphere into the ionosphere, and also for typical midlatitude daytime ionospheric conditions. It is shown that in the lower ionosphere all ion species have the same temperature; however, in the topside ionosphere above about 400 km, ion species can display differential temperatures depending upon the balance between thermal conduction, heating by collision with electrons, cooling by collisions with the neutrals, and energy transfer by inter-ion collisions. Both the time evolution and steady-state distribution of such ion temperature differentials are discussed.The results show that below 300km both the electrons and ions respond rapidly (<30s) to variations in direct thermal forcing. Above 600 km the electrons and ions display quite different times to reach steady state, depending on the electron density: when the electron density is low the electrons reach steady state temperatures in 30 s, but typically require 700 s when the density is high; the ions, on the other hand, reach steady state in 700 s when the density is high, and 1500–2500 s when the density is low. Between 300 and 600 km, a variety of thermal structures can exist, depending upon the electron density and the type of thermal forcing; however steady state is generally reached in 200–1000 s.     

Helium ion outflow from the terrestrial ionosphere

Extensive calculations have been made of the behaviour of He⁺ for situations where ion outflow occurs from the topside ionosphere. For these circumstances, steady state solutions for the He⁺ continuity, momentum and energy equations have been obtained self-consistently, yielding density, velocity and temperature profiles of He⁺ from 200 to 2000 km altitude. To model the high latitude topside ionosphere, a range of background H⁺O⁺ ionospheres was considered with variations in the H⁺ outflow velocity, the presence of a perpendicular electric field and different peak O⁺ densities. In addition, the atmospheric density of neutral helium was chosen to model typical observed winter and summer densities. From our studies we have found that: (a) The outflowing He⁺ has density profiles of similar shape to those of H⁺, for basically different reasons; (b) The effect of the perpendicular electric field differs considerably for H⁺ and He⁺. This difference stems from the fact that an electric field acts to alter significantly the O⁺ density at high altitudes and this, in turn, changes the H⁺ escape flux through the O⁺+H charge exchange reaction. A similar situation does not occur for He⁺ and therefore the He⁺ escape flux exhibits a negligibly small change with electric field; (c) The fractional heating of He⁺ due to the He⁺O⁺ relative flow is not as effective in heating He⁺ as the H⁺O⁺ relative flow is in heating H⁺; (d) During magnetospheric disturbances when the N₂ density at the altitude of the He⁺ peak (600 km) can increase by a factor as large as 50, the He⁺ peak density decreases only by approximately a factor of 2; and (e) The He⁺ escape flux over the winter pole is approximately a factor of 20 greater than the He⁺ escape flux over the summer pole. Consequently, on high latitude closed field lines there could be an interhemispheric He⁺ flux from winter to summer.     

Effects of Wave-Particle Interactions on Double-Hump Distributions of the H + Polar Wind

A Monte Carlo simulation is used in order to study the effects of wave-particle interactions (WPI) on H⁺ distributions in the polar wind outflow. The simulation also considers effects of the gravity, the polarization electric field, the divergence of geomagnetic field lines and H⁺−O⁺ Coulomb collisions. The proton velocity distribution function (VDF) and the profiles of its moments (density, bulk velocity, parallel and perpendicular temperatures, heat flux…) are found for different levels of WPI, i.e., for different values of the normalized diffusion rate in the velocity space (D _⊥). We find that the wave-particle interactions accelerate the polar wind and can have important effects on the double-hump H⁺ distribution obtained in the transition region between the collision-dominated low altitudes and the collisionless high altitude regions.     

Observations concerning the relationship between the quiet-time ring current and electron temperatures at trough latitudes

The relationship between the simultaneously observed positions of the maximum omnidirectional flux of the quiet-time ring current positive ions (Λ_φ) and the maximum electron temperature Λ_T in the trough is studied in the midnight sector of the topside ionosphere. Λ_φ maps to the inner edge of the plasma sheet where ring current fluxes change from nearly isotropic to trapped. At altitudes near 2500 km, the electron temperature at trough latitudes were always sharply peaked. Although Λ_φ varied with the level of geomagnetic activity, (Λ_φ ? Λ_T) did not. These observations support the hypothesis that the quiet-time ring current is the source of elevated electron temperatures found near the plasmapause. Below 1300 km, peaked electron temperature distributions in the trough were not consistent features of the data. It is shown that (Λ_φ ? Λ_T) increased with decreasing altitude. The possible influences of a westward component to the convective electric field and ionospheric refraction of ion cyclotron waves are discussed.