J. C. G. Walker

Theoretical ion densities in the lower ionosphere

Abstract We have solved the coupled momentum and continuity equations for NO + , O 2 + , 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 O 2 + 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.

THERMAL DIFFUSION IN THE TOPSIDE IONOSPHERE FOR MIXTURES WHICH INCLUDE MULTIPLY CHARGED IONS.

Abstract We have evaluated thermal diffusion coefficients for a fully ionized plasma containing a mixture of ions of arbitrary charge in which two ions may have densities comparable to the electron density. In order to illustrate the ionospheric effects of thermal diffusion we have calculated diffusive equilibrium density profiles in the topside ionosphere for O + , H + , N + , He + , O 2+ and N 2+ ions. The influence of thermal diffusion on the doubly-charged ions is particularly large, increasing their densities by more than two orders of magnitude at 1900 km.

Ionospheric electron densities and temperatures in aurora.

Abstract Electron density profiles corresponding to chemical equilibrium, and electron temperatures corresponding to heating of ambient electrons by auroral secondaries have been computed for five stable auroral arc systems with published height profiles of λ 3914 volume emission rates. The maximum electron density varies approximately as the three-quarters power of the λ 3914 intensity while the maximum temperature varies remarkably little. For these five auroras the temperature maxima lie between 2920°K and 3511°K and occur at altitudes between 330 km and 390 km.

Ion velocity distributions in the auroral ionosphere

Abstract 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.

THERMAL DIFFUSION IN THE F2 REGION OF THE IONOSPHERE.

Abstract In order to examine the effects of thermal diffusion on F 2-region ion densities we have evaluated ordinary and thermal diffusion coefficients to the second approximation of Chapman and Cowling for a partially ionized atomic oxygen plasma. Our results show that the thermal ambipolar diffusion coefficient, like the ordinary ambipolar diffusion coefficient, is not significantly affected by the electrons. Its value is determined almost entirely by ion-neutral interactions. We have solved the steady state continuity equation of the oxygen ions for typical mid-latitude daytime conditions and find that thermal diffusion acts to reduce the ion density at 600 km by 24 per cent. At altitudes above 300 km diffusion of the minor ions, H + , He + and N + is not influenced by the neutral species, and the ordinary and thermal diffusion coefficients of these ions may be evaluated for a fully ionized plasma. Our solutions of the continuity equations of these ions show that, at 700 km, the effect of thermal diffusion is to reduce the density of H + ions by 46 per cent, to reduce the density of He+ ions by 22 per cent, and to increase the density of N + ions by more than a factor of 2.

Secondary electrons in aurora

Abstract The Bethe approximation is used with measured and theoretical values of ionization cross sections and measured values of differential oscillator strengths to derive the initial energy spectrum of auroral secondary electrons. The differential flux of the auroral secondaries is then calculated, using the approximation of continuous energy loss. The calculations are applied to a particular aurora for which rocket data have been published. There is substantial disagreement between theoretical and measured electron spectra. The theoretical spectra show structure at energies less than 20 eV, associated primarily with vibrational and electronic excitation of molecular nitrogen. This structure is largely absent in the measured spectrum. Substantially more high energy electrons were measured than theory predicts. In addition, there are disagreements in the altitude profiles of the total number of non-thermal secondary electrons. Calculated values of OI green line photon emission rates which result from excitation by secondary electrons and dissociative recombination of O 2 + fall short of the measured values. The effect on the excitation rate of varying several parameters is investigated, and it is found that the results are particularly sensitive to competing inelastic processes in N 2 .

TRANSPORT PROPERTIES OF THE IONOSPHERIC ELECTRON GAS.

Abstract We have evaluated the transport coefficients of the ionospheric electron gas—thermal conductivity, electrical conductivity, current flow conductivity due to thermal gradients, and heat flow conductivity due to electric fields. Shkarofskys formulation has been used, making it possible to allow rigorously for the velocity dependence of electron-electron, electron-ion, and electron-neutral collision frequencies. This has permitted us to calculate the transport coefficients at all altitudes from the weakly-ionized limit at 100 km to the fully-ionized limit at 600 km. In this way we confirm the accuracy of an expression for the thermal conductivity in the ionosphere derived by Banks, but we find an error in the expression for the electrical conductivity which has been used in some ionospheric studies. We explore possible thermoelectric effects on ionospheric electron temperatures and conclude that temperatures are significantly affected by field-aligned currents of about 10−5 amp m−2, such as appear to flow in the auroral oval.

The effect of oxygen cooling on ionospheric electron temperatures

Abstract There are discrepancies between ionospheric electron temperatures derived from Thomson scatter data and electron temperatures predicted from the solar ultra-violet heat source. The inclusion of electron cooling by excitation of the fine-structure levels of atomic oxygen removes the discrepancy throughout the day at all altitudes above 320km. Below this altitude a discrepancy persists, but it probably lies within the uncertainties arising from the basic atomic and molecular data employed in the theoretical analysis and from the solar-flux data.

Minor ion diffusion in the F2-region of the ionosphere

Abstract We have evaluated ionospheric diffusion coefficients to the second approximation of Chapman and Cowling in order to check the first approximation values which are currently in use. We find that the first approximation to the ambipolar diffusion coefficient is quite accurate, but that similar diffusion coefficients for the minor ions are in error by as much as a factor of 2. Coulomb collisions couple minor ion drift velocities closely to the velocity of the O+ ions. Consequently, minor ion densities in the F-region are very sensitive to fluxes of ionization into or out of the ionosphere. To illustrate this sensitivity we present solutions of the continuity equations for O+, H+, He+ and N+ ions in the F-region for a range of topside boundary conditions. We find that H+ densities are significantly reduced if the upward O+ flux approaches 9 × 108 cm −2 sec−1 or if the upward H+ flux approaches 2·5 × 107 cm−2 sec−1. For He+ the corresponding limits are 4 × 108 cm−2 sec−1 of O+ or 4.3 × 106 cm−2 sec−1 of He+, and for N+ the limits are 2 × 108 cm−2 sec−1 of O+ or 9.5 × 105 cm−2 sec−2 of N+.

The influence of field-aligned currents on auroral electron temperatures

Abstract A precipitating flux of auroral electrons produces a flow of reverse current to maintain electrical neutrality in the ionosphere. The transport effects associated with such a current act as heat sinks for the electron gas, resulting in auroral electron temperatures that are lower at high altitude than they would be in the absence of the current. In a typical aurora the difference approaches 1000°K above 700 km. There are electric fields associated with the parallel currents but their magnitude is only a few microvolts per meter.