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.     

Asymmetry of plasma fluxes at Mars. ASPERA-3 observations and hybrid simulations

The asymmetry of fluxes of solar wind and planetary ions is studied by using the ASPERA-3 observations onboard the Mars Express spacecraft in February 2004 to March 2006. Due to the small scale of the Martian magnetosphere and its induced origin, the flow pattern near Mars is sensitive to the directions of the interplanetary magnetic and electric (-V×B) fields. Asymmetry of the magnetic field draping produces an asymmetry in plasma flows in the plane containing the IMF. The crustal magnetic fields on Mars also influence the flow pattern. Scavenging of planetary ions is less efficient in the regions of strong crustal magnetization and therefore the escape fluxes of planetary ions in the southern hemisphere are smaller. The results of the observations are compared to simulations based on a 3D hybrid model with several ion species.     

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.     

Behaviour of ion velocity distributions for a simple collision model

For application to studies of the high latitude ionosphere, we have calculated ion velocity distributions for a weekly-ionized plasma subjected to crossed electric and magnetic fields. An exact solution to Boltzmann's equation has been obtained by replacing the Boltzmann collision integral with a simple relaxation model. At altitudes above about 150 km, where the ion collision frequency is much less than the ion cyclotron frequency, the ion distribution takes the shape of a torus in velocity space for electric fields greater than 40 mV m^?1. This shape persists for 1–2 hr after application of the electric field. At altitudes where the ion collision and cyclotron frequencies are approximately equal (about 120 km), the ion velocity distribution is shaped like a bean for large electric field strengths. This bean-shaped distribution persists throughout the lifetime of ionospheric electric fileds. These highly non-Maxwellian ion velocity distributions may have an appreciable affect on the interpretation of ion temperature measurements.     

The calculated and observed diurnal variation of the ionosphere over Millstone Hill on 23–24 March 1970

A numerical model of current F-region theory is use to calculate the diurnal variation of the mid-latitude ionospheric F-region over Millstone Hill on 23–24 March 1970, during quiet geomagnetic conditions. From the solar EUV flux, the model calculates at each altitude and time step primary photoelectron spectra and ionization rates of various ion species. The photoelectron transport equation is solved for the secondary ionization rates, photoelectron spectra, and various airglow excitation rates. Five ion continuity equations that include the effects of transport by diffusion, magnetospheric-ionospheric plasma transport, electric fields, and neutral winds are solved for the ion composition and electron density. The electron and ion temperatures are also calculated using the heating rates determined from chemical reactions, photoelectron collisions, and magnetospheric-ionospheric energy transport. The calculations are performed for a diurnal cycle considering a stationary field tube co-rotating with the Earth; only the vertical plasma drift caused by electric fields perpendicular to the geomagnetic field line is allowed but not the horizontal drift. The boundary conditions used in the model are determined from the incoherent scatter radar measurements of T_e, T_i and O⁺ flux at 800km over Millstone Hill (Evans, 1971a). The component of the neutral thermospheric winds along the geomagnetic field has an important influence on the overall ionospheric structure. It is determined from a separate dynamic model of the neutral thermosphere, using incoherent scatter radar measurements.The calculated diurnal variation of the ionospheric structure agrees well with the values measured by the incoherent scatter radar when certain restrictions are placed on the solar EUV flux and model neutral atmospheric compositions. Namely, the solar EUV fluxes of Hinteregger (1970) are doubled and an atomic oxygen concentration of at least $\text{10}{}^{11}\text{cm}{}^3$ at 120 km is required for the neutral model atmosphere. Calculations also show that the topside thermal structure of the ionosphere is primarily maintained by a flow of heat from the magnetosphere and the night-time F2-region is maintained in part by neutral winds, diffusion, electric fields, and plasma flow from the magnetosphere. The problem of maintaining the calculated night-time ionosphere at the observed values is also discussed.     

A new method for generating instantaneous ionospheric conductivity models using ground-based magnetic data

We have developed a dynamical model of the ionospheric conductivity distribution using ground magnetic data. The model is based on the Spiro et al. (1982, J. geophys. Res. 87, 8215) average conductivity models, but adjusts their latitudinal distribution to the instantaneous distribution of field-aligned currents calculated from the equivalent current function. It can thus take into account the dependence of the conductivity distribution on fluctuations of solar wind parameters and magnetospheric disturbances. A comparison of electric fields calculated from the equivalent current function and the new conductivity model with those measured by the STARE radars, shows that the present conductivity model gives better results than obtained by using the same current function but earlier conductivity models.     

Energy balance in a magnetically confined coronal structure observed by OSO-7

A model of a coronal region of enhanced Fexv and Fexvi emission is developed and its energy balance is examined using extreme ultraviolet observations from OSO-7 together with calculations of possible force-free coronal magnetic field configurations. The coronal emissions overlying the photospheric boundary between regions of opposite magnetic polarity are found to be associated with generally non-potential (current-carrying) magnetic fields in the forms of arches with footpoints in regions of opposite polarity. The orientation of these arches relative to the neutral line changes with degree of ionization of the emitting ion (which we infer from our limb observations to be a function of height) and may be evidence of differing electric currents along various field lines. The appearance of a coronal arch, seen side-on, can conveniently be represented by a parabola and a detailed analysis (Appendix) shows this to be a realistic approximation that should be generally useful in analyzing two-dimensional pictures of coronal structures. Applying this analysis to the most prominent coronal region observed in the radiations of Fexv and Fexvi, we find a maximum in the electron temperature, T _e , of 2.6 × 10⁶K at the top of arches whose heights are 20000–40000 km and whose footpoints are separated by ≈ 100000 km. A temperature gradient of ▽T _e ≈5 × 10^-5K cm^-1 is found in this coronal structure. Radiative losses are typically fifteen times greater than conductive losses and the energy deposition required to maintain the coronal feature is nearly uniformly distributed along its length.     

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.     

Electric fields within the martian magnetosphere and ion extraction: ASPERA-3 observations

Observations made by the ASPERA-3 experiment onboard the Mars Express spacecraft found within the martian magnetosphere beams of planetary ions. In the energy (E/q)-time spectrograms these beams are often displayed as dispersive-like, ascending or descending (whether the spacecraft moves away or approach the planet) structures. A linear dependence between energy gained by the beam ions and the altitude from the planet suggests their acceleration in the electric field. The values of the electric field evaluated from ion energization occur close to the typical values of the interplanetary motional electric field. This suggests an effective penetration of the solar wind electric field deep into the martian magnetosphere or generation of large fields within the magnetosphere. Two different classes of events are found. At the nominal solar wind conditions, a ‘penetration’ occurs near the terminator. At the extreme solar wind conditions, the boundary of the induced magnetosphere moves to a more dense upper atmosphere that leads to a strong scavenging of planetary ions from the dayside regions.     

On the dynamics of the jovian ionosphere and thermosphere.: IV. Ion-neutral coupling

We use the fully coupled, three-dimensional, global circulation Jovian Ionospheric Model (JIM) to calculate the coupling between ions in the jovian auroral ovals and the co-existing neutral atmosphere. The model shows that ions subject to drift motion around the auroral oval, as a result of the E×B coupling between a meridional, equatorward electric field and the jovian magnetic field, generate neutral winds in the planetary frame of reference. Unconstrained by the magnetic field, these neutral winds have a greater latitudinal extent than the corresponding ion drifts. Values of the coupling coefficient, k(h), are presented as a function of altitude and cross-auroral electric field strength, for different incoming electron fluxes and energies. The results show that, with ion velocities of several hundred metres per second to over 1 km s⁻¹, k(h) can attain values greater than 0.5 at the ion production peak. This parameter is key to calculating the effective conductivities required to model magnetosphere-ionosphere coupling correctly. The extent to which angular momentum (and therefore energy) is transported vertically in JIM is much more limited than earlier, one-dimensional, studies have predicted.     

Time-dependent behaviour of a stable auroral red arc excited by an electric field

We examine the electric field hypothesis as a possible explanation of a stable auroral red arc. An electric field perpendicular to the geomagnetic field in the ionosphere heats the ambient F-region electrons and ions. Given large enough electric fields, the electrons can be heated sufficiently to excite the OI (¹D) term of atomic oxygen by electron impact, giving rise to the λ6300 emission characteristic of the red arc. The electron and ion heating rates are determined by the relative drift between the plasma and neutral gas.     

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.     

Collisionless Magnetic Reconnection in the Presence of Initial Guide Field

By using the method of 2-dimensional, 3-component full particle simulation, collisionless magnetic reconnection in the presence of various initial guide fields and the Harris current sheet with 1-dimensional initial state are studied. The results show that strong guide fields with B_z0 > 0.5B₀ can evidently alter not only the trajectory of the particles, but also the structure of the electric and velocity fields in the vicinity of the reconnection region, thereby affecting the rate of reconnection and the acceleration of electrons. The generalized Ohm's law is employed to interpret the structural characteristics of the electric fields with various guide fields. Also, via the tracing of the electron beam near he diffusion region, it is revealed that in the 2-D model, for both strong and weak guide fields, the induced electric field perpendicular to the simulation plane at the center of the diffusion region plays the major role in the acceleration of electrons. The contribution of the planar electric field outside the diffusion region is very small.     

Localized auroral disturbance in the morning sector of topside ionosphere as a standing electromagnetic wave

An intense, localized auroral disturbance observed by Intercosmos-Bulgaria-1300 satellite in the morning sector at the altitude 850 km is analyzed in detail. The disturbance is characterized by strong “jumps” of electric and magnetic fields reaching ～ 80 mV/m and ～ 100 nT, fluctuations of ion density (Δn/n ～ 70%) and bursts of downward and upward energetic electron fluxes. Electric and magnetic disturbances display a distinct spatial-temporal relationship typical for the standing quasi-monochromatic wave ($\text{? ～ 1}\text{Hz}\text{, λ}{}_{\mathrm{x}}\text{～ 10}\text{km}$). The ratio of amplitudes of electric and magnetic fluctuations is equal to Alfvén velocity (ΔE/ΔB ～ v_A/c). However, a strong parallel component of the electric field (～ 30 mV/m) and large ion density fluctuations indicate significant changes of plasma properties (the effects of anomalous resistivity are possible).     

Observations of energetic ions in inverted V events

Simultaneous measurements of keV ions and electrons with the ESRO 1A satellite have shown the following ion characteristics among others. Ions of about 6 keV energy are strongly field-aligned on the flanks of the inverted V events (mainly through the disappearance of the ion flux near 90° pitch angle). Field-aligned electron fluxes are often found in the same regions of the inverted V events where the ions are field-aligned. At the centre of inverted V events isotropization occurs (except in some small events). The 1 keV ion flux at large pitch angles (80°) is generally not reduced very much when the 6 keV, 80° ion flux shows strongly decreased values. The ratio of the 1 to 6 keV ion flux has a maximum near the centre of an inverted V event where the electron spectrum is hardest and the 6 keV ions are isotropic (or nearly isotropic).The observations are interpreted in terms of a model with two oppositely directed field-aligned electrostatic potential drops: one upper accelerating electrons downward and one lower, produced by the electron influx, which accelerates ions downward. Ion scattering in turbulent wave fields is proposed to be responsible for the observation that the 1 keV ion flux at large pitch angles does not decrease strongly where the 6 keV ion flux does and as an explanation of the isotropization at the centre of the event. The source problem for the ions is eliminated by the precipitating electrons ionizing continuously the thin neutral atmosphere even at altitudes of a few thousand kilometers.     

Dynamical interpretation of observed plasmasphere deformations

Based on all of the OGO-5 light ion density measurements (covering the period from March, 1968 to May, 1969), a definition of “isolated plasma regions” was employed to locate the most prominent patches of enhanced light ion densities in the midst of the depleted region, outside of the main plasmasphere. On the dayside, the distribution of these isolated plasma in L.T. vs. L coordinates was quite similar to that of the “detached plasma regions” by Chappell (1974a). On the nightside, however, the new distribution revealed more frequent occurrence of these regions. Elongated thick plasmatails produced during periods of sudden enhancement of convection electric fields and subsequentially thinning and corotating of the plasmatails during quieting periods, in general, could account for the statistical distribution as well as the individual events, such as those between March 27 and April 2, 1968 and Oct. 21 and Oct. 24, 1968. As demonstrated by Kivelson (1976), wave-particle interactions could produce tremendously complicated structures observed in the near vicinity of the plasmapause and far away from the plasmasphere. Examination of H⁺ and He⁺ density measurements for period of Aug. 12–Aug. 20, 1968 indicated that the density reduction of the plasmasphere during a magnetic storm was on the same order of magnitude as that obtained from whistler techniques during a magnetospheric substorm.     

Effects of convection electric field on the distribution of ring current type protons

The topology of the boundaries of penetration (or inversely the boundaries of the forbidden regions) of 90° pitch angle equatorial protons with energies less than 100 keV are explored for an equatorial convection E-field which is directed in general from dawn to dusk. Due to the dependence of drift path on energy (or magnetic moment) complex structural features are expected in the proton energy spectra detected on satellites since the penetration distance of a proton is not a monotonically increasing or decreasing function of energy. During a storm when the convection E is enhanced, model calculations predict elongations of the forbidden regions analogous to plasmatail extensions of the plasmasphere. Following a reduction in the convection field, spiral-structured forbidden regions can occur. Structural features inherent to large scale convection field changes may be seen in the noselike proton spectrograms observed near dusk by instrumentation on the satellite Explorer 45 (S³) (Smith and Hoffman, 1974). These nose events are modelled by using an electric field model developed originally by Volland (1973). The strength of the field is related to K_p through night-time equatorial plasmapause measurements.     

Fine structure of solar magnetic fields

The problem of inequality of results of longitudinal magnetic fields measured in the magnotosensetive lines FeI 5250 and FeI 5247 is investigated. The observed ratio of longitudinal components of magnetic field H ₁₁(5250)/H ₁₁(5247) is compared to the calculated for different combinations of magnetic field elements. The calculations have been made with standard model photosphere for quiet regions. It was concluded that the underestimated value of magnetic field obtained with the FeI 5250 line is explained by the presence of unresolved elements with kilogauss magnetic fields.