Mid-latitude electron content modelling: The role of interhemispheric coupling

A modelling study of the electron content of the mid-latitude ionosphere and protonosphere has been carried out for solstice conditions using the mathematical model of Bailey (1983). In the model calculations coupled time-dependent O⁺, H⁺ continuity and momentum equations and O⁺, H⁺ and electron heat balance equations are solved for a magnetic shell extending over both hemispheres. The inclusion of interhemispheric flow of plasma and of heat balance has enabled us to investigate the role of interhemispheric coupling on the electron content and related shape parameters. The computed results are compared with results from slant path observations of the ATS-6 radio beacon made at Lancaster (U.K.) and Boulder, Colorado (U.S.A.).It has been found that the conjugate photoelectron heating has a major effect on the shape of the daily variation of slant slab thickness (τ) and also on the magnitude of the protonospheric content (N_p). Some of the main features of τ are closely related to the sunrise and sunset times in the conjugate ionosphere. Also it is found that night-time increases in total electron content (N_T) and F2 region peak electron density (N_max) in winter are natural consequences of ionization loss at low altitudes causing an enhanced downward flow of plasma from the protonosphere which is coupled to the summer hemisphere. One other important consequence of the coupled protonosphere is that the effects on N_T of the neutral air wind are not much different in winter from those in summer.     

Nighttime proton fluxes at Millstone Hill

Incoherent scatter measurements of electron density and vertical O⁺ fluxes over Millstone Hill (42.6°N, 71.5°W) previously have been used to study the exchange of plasma between the ionosphere and the magnetosphere. During the daytime there is usually an upward flux of O⁺ ions above about 450 km that can be measured readily and equated to the escaping proton flux. At night the O⁺ fluxes usually are downwards everywhere owing to the decay of the F-layer, and it becomes difficult to detect effects due an arriving proton flux. In a new study of the nighttime fluxes, appeal was made to the estimated abundance of the H⁺ ions in the upper F-region which can be extracted from the observations. From a study of the behavior on 25 days over the interval 1969–1973, we conclude that in the daytime the flux always is upwards and close to its limiting value. This situation persists throughout the night in summer at times of high sunspot activity (e.g., 1969). There is a period of downward flux prior to ionospheric sunrise on winter nights whose duration increases with decreasing sunspot number. As sunspot minimum is approached (e.g., in 1973) downward fluxes are encountered for a brief period prior to ionospheric sunrise in summer also. Thus, over most parts of sunspot cycle, it appears that the protonosphere supplies ionization to the winter night ionosphere, while being maintained from the summer hemisphere. This helps explain the smallness of the day-to-night variations reported for the electron content of magnetospheric flux tubes near L = 4 in the American sector.     

Induced proton flow in a collapsing post-sunset ionosphere and protonosphere

The effect of the onset of post-sunset conditions on thermal proton flow is examined for mid-latitudes by numerical solution of the equations of continuity, momentum and energy balance for H⁺ and O⁺. Results are calculated for a dipole magnetic field tube situated at L = 4 and acceleration terms are included in the momentum equations. Proton flow into the ionosphere results from decay of the F2-layer. Changes in temperatures and temperature gradients following sunset may not enhance the H⁺ flow. Under extreme conditions the H⁺ flow remains subsonic. It seems unlikely that an interhemispheric flux of protons can directly maintain the nighttime F2-layer.     

The topside equatorial ionosphere during daytime: Elevated plasma temperatures,the transequatorial O+ breeze and the dynamics of minor ions

Steady-state calculations are performed for the daytime equatorial F2-region and topside ionosphere. Values are calculated of the electron and ion temperatures and the concentrations and field-aligned velocities of the ions O⁺, H⁺ and He⁺. Account is taken of upward $\text{E × B}$ drift, a summer-winter horizontal neutral air wind and heating of the electron gas by thermalization of fast photoelectrons.The calculated plasma temperatures are in accord with experiment: at the equator there is an isothermal region from about 400–550 km altitude, with temperatures of about 2400 K around 800 km altitude. The transequatorial O⁺ breeze flux from summer to winter in the topside ionosphere is not greatly affected by the elevated plasma temperatures. The field-aligned velocities of H⁺ and He⁺ depend strongly on the O⁺ field-aligned velocity and on the presence of large temperature gradients. For the minor ions, ion-ion drag with O⁺ cannot be neglected for the topside ionosphere.     

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 photoelectron heating and interhemisphere transport on day-time plasma temperatures at low latitudes

The thermal balance of the plasma in the day-time equatorial F region is examined. Steady-state solutions of electron and ion temperatures are obtained, assuming the ions are O⁺ and H⁺. The theoretical concentrations of O⁺ and H⁺ and the field-aligned velocity were obtained following Moffett and Hanson (1973), while theoretical photoelectron heating rates of the electron gas were taken from Swartz et al. (1975).The results demonstrate the gross features in the electron and ion temperatures as observed at the Jicamarca Observatory and in the ion temperatures observed on the OGO-6 satellite. The rapid increase in electron temperature above 500 km at the magnetic equator is due to heating by photoelectrons created at higher latitudes and travelling up along the field lines. The rapid increase in ion temperature is due to good thermal contact with the electrons rather than the neutrals. It is shown that field-aligned interhemispheric thermal plasma flows appreciably affect these temperatures, and that, with a net plasma flow from the summer hemisphere to the winter hemisphere, the temperatures are higher in the winter hemisphere. These effects are related to the character of the ion temperature minimum observed by OGO-6 near the magnetic equator.     

Coupling between the F-region and protonosphere: Numerical solution of the time-dependent equations

This paper describes a new method of solution of the time-dependent continuity and momentum equations for H⁺ and O⁺ in mid-latitude magnetic field tubes from the F-region to the equator. For each ion the equations are expressed as an integro-differential equation. This equation is treated as an ordinary differential equation and solved by a searching method. By means of this method, the distribution of H⁺ in the O⁺?H⁺ transition region and the protonosphere can be investigated and the influence of H⁺ fluxes on the F layer examined.As an example of application of the method a suggestion by Park (1971) about observed night-time enhancements of N_mF2 is examined. He suggested that lowering of the F layer some hours after a magnetic substorm may cause N_mF2 to increase because of increased ion influx from the protonosphere. In the present calculations the Flayer is maintained around a constant height for some time and then abruptly lowered. Under the conditions adopted the resulting increase in downward H⁺ flux is sufficient to maintain N_mF2 against the increased recombination but not to increase N_mF2 significantly. It is emphasised that these results are not conclusive.     

The transient response of the topside ionosphere to precipitation

A numerical time-dependent model of the topside and F-layer ionosphere is used to describe how the density of O⁺ ions and the plasma temperatures change as a result of transient electron precipitation with a soft energy spectrum (ca. 100 eV per electron). The response time for electron gas heating is about 2 min; for changes in topside scale height it is from 5 to 15 min, depending on altitude; and for changes in F-layer peak density, it is more than an hour. The low-density topside ion gas is thermally isolated on a short time scale; consequently the ion temperature responds almost adiabatically to volume changes. A transient precipitation event (of, say, 10 min duration) initiates a disturbance that propagates upward at approximately the sonic upeed in the plasma (ca. 2km/s), growing in amplitude with height. Such an event has little effect on the density at the peak of the F layer. An element of ionosphere that drifts horizontally in an antisunward direction through the magnetospheric cleft and into the polar cap recieves some ionization from the cleft, but not enough to be decisive in its survival. The collapse of the topside when heating is removed increases temporarily the density of the F layer.     

Effects of convection electric field on the thermal plasma flow between the ionosphere and the protonosphere

Dynamic behavior of the coupled ionosphere-protonosphere system in the magnetospheric convection electric field has been theoretically studied for two plasmasphere models. In the first model, it is assumed that the whole plasmasphere is in equilibrium with the underlying ionosphere in a diurnal average sense. The result for this model shows that the plasma flow between the ionosphere and the protonosphere is strongly affected by the convection electric field as a result of changes in the volume of magnetic flux tubes associated with the convective cross-L motion. Since the convection electric field is assumed to be directed from dawn to dusk, magnetic flux tubes expand on the dusk side and contract on the dawn side when rotating around the earth. The expansion of magnetic flux tubes on the dusk side causes the enhancement of the upward H⁺ flow, whereas the contraction on the dawn side causes the enhancement of the downward H⁺ flow. Consequently, the H⁺ density decreases on the dusk side and increases on the dawn side. It is also found that significant latitudinal variations in the ionospheric structures result from the L-dependency of these effects. In particular, the H⁺ density at 1000 km level becomes very low in the region of the plasmasphere bulge on the dusk side. In the second model, it is assumed that the outer portion of the plasmasphere is in the recovery state after depletions during geomagnetically disturbed periods. The result for this model shows that the upward H⁺ flux increases with latitude and consequently the H⁺ density decreases with latitude in the region of the outer plasmasphere. In summary, the present theoretical study provides a basis for comparison between the equatorial plasmapause and the trough features in the topside ionosphere.     

The topside ionosphere above Arecibo at equinox during sunspot maximum

The coupled time-dependent O⁺ and H⁺ continuity and momentum equations and O⁺, H⁺ and electron heat balance equations are solved simultaneously within the L = 1.4 (Arecibo) magnetic flux tube between an altitude of 120 km and the equatorial plane. The results of the calculations are used in a study of the topside ionosphere above Arecibo at equinox during sunspot maximum. Magnetically quiet conditions are assumed.The results of the calculations show that the L = 1.4 magnetic flux tube becomes saturated from an arbitrary state within 2–3 days. During the day the ion content of the magnetic flux tube consists mainly of O⁺ whereas O⁺ and H⁺ are both important during the night. There is an altitude region in the topside ionosphere during the day where ion-counterstreaming occurs with H⁺ flowing downward and O⁺ flowing upward. The conditions causing this ion-counterstreaming are discussed. There is a net chemical gain of H⁺ at the higher altitudes. This H⁺ diffuses both upwards and downwards whilst O⁺ diffuses upwards from its solar e.u.v. production source which is most important at the lower altitudes. During the night the calculated O⁺ and H⁺ temperatures are very nearly equal whereas during the day there are occasions when the H⁺ temperature exceeds the O⁺ temperature by about 300 K.     

Thermal proton flow in the plasmasphere: The morning sector

Vertical profiles of electron density obtained in the vicinity of the plasmapause using the Alouette-II topside sounder have been analyzed to assess the presence of H⁺ flow in the topside ionosphere. The observations in the midnight sector show clearly the presence of the plasmapause; i.e. there is a sharp boundary separating the poleward regions of polar wind H⁺ flow and the more gentle conditions of the plasmasphere where light ions are present in abundance. In contrast, in the sunlit morning sector upwards H⁺ flow is deduced to be present to invariant latitudes as low as 48° (L = 2·2) in the regions normally known to be well inside the plasmasphere. The upwards H⁺ flux is sufficiently large (3 × 10⁸ ions cm^?2 sec^?1) that the plasmapause cannot be seen in the latitudinal electron density contours of the topside ionosphere. The cause for this flow remains unknown but it may be a result of a diurnal refilling process.     

Modelling of thermospheric composition changes caused by a severe magnetic storm

The UCL 3-dimensional time-dependent thermospheric model, with atomic and molecular components, is used to study composition changes in the neutral gas at F-layer heights produced by a severe magnetic storm. The computations give the mean molecular weight (MW), temperature and winds as functions of latitude, longitude, height and time for a period of 30 h.Starting from quiet-day conditions, the simulation starts with a 6-h “substorm” period in which strong electric fields are imposed in the auroral ovals, accompanied by particle input. Weaker electric fields are imposed for the remaining 24 h of the simulation. The energy input causes upwelling of air in the northern and southern auroral ovals, accompanied by localized composition changes (increases of MW), which spread no more than a few hundred kilometres from the energy sources. There is a corresponding downward settling of air at winter midlatitudes and low latitudes, producing widespread decreases of MW at a fixed pressure-level. These storm effects are superimposed on the quiet-day summer-to-winter circulation, in which upwelling occurs in the summer hemisphere and down welling in the winter hemisphere. The composition changes seen at a fixed height differ somewhat from those at a fixed pressure-level, because of the expansion resulting from the storm heating.The results can be related to the well-known prevalence of “negative” F-layer storms (with decreases of F2-layer electron density) in summer, and “positive” F-layer storms in winter and at low latitudes. However, the modelled composition changes are not propagated far enough to account for the observed occurrence of negative storms at some distance from the auroral ovals. This difficulty might be overcome if particle heating occurs well equatorward of the auroral ovals during magnetic storms, producing composition changes and negative storm effects at midlatitudes. Winds do not seem a likely cause of negative storm effects, but other factors (such as increases of vibrationally-excited N₂) are possibly important.     

A study of F2 region daytime vertical ionization fluxes at Millstone Hill during 1969

A study has been undertaken of the vertical fluxes of ionization in the F2 region over Millstone Hill (L = 3.2) utilizing incoherent scatter measurements of electron density, electron and ion temperatures, ion composition and vertical velocity, made over 24-hr periods twice per month during 1969. The paper presents the results for all these parameters on five representative days, and discusses the distribution of the vertical flux observed during the daytime at other times during the year.Near noon the downward flux reached a peak near 300 km with an average value of ～3 × 10⁹ el/cm²/sec in winter and ～1.6 × 10⁹ el/cm²/sec in summer. The difference is thought to be real and be caused by the higher loss rates prevailing in summer. Above 550 km there is usually a transition to upward flux, which appears to be fully established by 700 km and has an average value of the order of 5 × 10⁷ l/cm²/sec. From ion composition measurements, it appears that this flux is carried almost entirely by O⁺ ions to at least ～900 km, as the H⁺ ion concentration is small (<2% at ～775 km altitude) in this region by day. While the value of the escape flux appears in fair agreement with theoretical estimates of the limiting flux for this portion of the sunspot cycle, the extremely low H⁺ concentrations do not appear to be in accord with existing models.The diurnal variation of the upward flux through 650 km exhibits an abrupt onset close to the time of sunrise at the 200 km level (χ = 103°). A reversal to downward flux usually begins before sunset, often in the early afternoon.     

The light ion trough

A distinct feature of the ion composition results from the OGO-2, 4 and 6 satellites is the light ion trough, wherein the mid latitude concentrations of H⁺ and He⁺ decrease sharply with latitude, dropping to levels of 10³ ions/cm³ or less near 60° dipole latitude (L=4). In contrast to the ‘main trough’ in electron density, N_e, observed primarily as a nightside phenomenon, the light ion trough persists during both day and night. For daytime winter hemisphere conditions and for all seasons during night, the mid latitude light ion concentration decrease is a pronounced feature. In the dayside summer and equinox hemispheres, the rate of light ion decrease with latitude is comparatively gradual, and the trough boundary is less well defined, particularly for quiet magnetic conditions. In response to magnetic storms, the light ion trough minimum moves equatorward, and deepens, consistent with earlier evidence of the contraction of the plasmasphere in response to storm time enhancements in magnetospheric plasma convection. The fact that a pronounced light ion trough is observed under conditions for which the dominant ion O⁺ may exhibit little or no simultaneous decrease appears to explain why earlier studies of the ‘main trough’ in topside distributions of N_e and N_i may, at times, have been inconclusive in relating the total ionization minimum with the mechanism of the plasmapause. In particular, the topside distribution of N_i appears to be the complex resultant of several variables within the ion composition, being governed by the competing processes of chemical production and loss, loss through magnetospheric convection, and large-scale dynamic transport resulting from neutral winds and electric fields. The net result is that in general, the light ion trough, rather than N_i, provides a more fundamental parameter for examining the structure and behavior of the plasmapause.     

A study of plasmaspheric density distributions for diffusive equilibrium conditions

We have modelled the plasmaspheric density distribution for a range of solar cycle, seasonal and diurnal conditions with a magnetic flux tube dependent diffusive equilibrium model by using experimentally determined values of ionospheric parameters at 675 km as boundary conditions.Data is presented in terms of plasmaspheric H⁺ and He⁺ density contours, total flux tube content and equatorial plasma density for a range of L-values from 1.15 to 3.0. The variation of equatorial density with L-value shows good agreement with the $\text{1}\text{L}{}^4$ dependence observed experimentally.The results show that the model predicts larger solar cycle and diurnal variation in equatorial plasma density than observed using whistler techniques. However, the whistler method requires a model to deduce the equatorial density and is therefore open to interpretation.Seasonal variations are rather artifical since in this general model we have not attempted to match equatorial densities for flux tubes emanating from the winter and summer hemispheres.     

Ion temperature troughs induced by a meridional neutral air wind in the night-time equatorial topside ionosphere

A mathematical model has been developed to calculate consistent values for the O⁺ and H⁺ concentrations and field-aligned velocities and for the O⁺, H⁺ and electron temperatures in the night-time equatorial topside ionosphere. Using the results of the model calculations a study is made to establish the ability of F-region neutral air winds to produce observed ion temperature distributions and to investigate the characteristics of ion temperature troughs as functions of altitude, latitude and ionospheric composition. Solar activity conditions that give exospheric neutral gas temperatures 600 K, 800 K and 1000 K are considered.It is shown that the O⁺-H⁺ transition height represents an altitude limit above which ion cooling due to adiabatic expansion of the plasma is extremely small. The neutral atmosphere imposes a lower altitude limit since the neutral atmosphere quenches any ion cooling which field-aligned transport tends to produce. The northern and southern edges of the ion temperature troughs are shown to be restricted to a range of dip latitudes, the limiting dip latitudes being determined by the magnetic field line geometry and by the functional form of the F-region neutral air wind velocity. Both these parameters considerably influence the interaction between the neutral air and the plasma within magnetic flux tubes.     

A numerical investigation of the formation and evolution of magnetospheric irregularities by the interchange of magnetic flux tubes

The formation and evolution of magnetospheric irregularities by interchange of tubes of force, is studied through the solution of the electron and ion heat, and ion density equations. These calculations indicate that interchange of magnetic flux tubes may cause irregularities in the ionosphere and protonosphere. Ionospheric irregularities result from disturbance of the F-layer through electrodynamic movement vertically while the protonospheric irregularities result from variations in flux tube volume. It has been found that the temperature profile plays an important role in the variation of irregularity magnitude along flux tubes and that irregularities will persist for many hours at night. After several hours a small growth of the irregularities has been observed.     

Ion transition heights from topside electron density profiles

Theoretical electron density profiles are calculated for the topside ionosphere to determine the major factors controlling the profile shape. Only the mean temperature, the vertical temperature gradient and the $\text{O}{}^{\mathrm{+}}\text{H}{}^{\mathrm{+}}$ ion transition height are important. Vertical proton fluxes alter the ion transition height but have no other effect on the profile shape. Diffusive equilibrium profiles including only these three effects fit observed profiles, at all latitudes, to within experimental accuracy.Values of plasma temperature, temperature gradient and ion transition height h_tT were determined by fitting theoretical models to 60,000 experimental profiles obtained from Alouette l ionograms, at latitudes of 75°S–85°N near solar minimum. Inside the plasmasphere h_T varies from about 500 km on winter nights to 850 km on summer days. Diurnal variations are caused primarily by the production and loss of O⁺ in the ionosphere. The approximately constant winter night value of h_T is close to the level for chemical equilibrium. In summer h_T is always above the equilibrium level, giving a continual production of protons which travel along lines of force to aid in maintaining the conjugate winter night ionosphere. Outside the plasmasphere h_T is 300–600 km above the equilibrium level at all times. This implies a continual near-limiting upwards flux of protons which persists down to latitudes of about 60° at night and 50° during the day.     

Dynamical behavior of thermal protons in the mid-latitude ionosphere and magnetosphere

Satellite and other observations have shown that H⁺ densities in the mid-latitude topside ionosphere are greatly reduced during magnetic storms when the plasmapause and magnetic field convection move to relatively low L-values. In the recovery phase of the magnetic storm the convection region moves to higher L-values and replenishment of H⁺ in the empty magnetospheric field tubes begins. The upwards flow of H⁺, which arises from O⁺—H charge exchange, is initially supersonic. However, as the field tubes fill with plasma, a shock front moves downwards towards the ionosphere, eventually converting the upwards flow to subsonic speeds. The duration of this supersonic recovery depends strongly on the volume of the field tube; for example calculations indicate that for L = 5 the time is approximately 22 hours. The subsonic flow continues until diffusive equilibrium is reached or a new magnetic storm begins. Calculations of the density and flux profiles expected during the subsonic phase of the recovery show that diffusive equilibrium is still not reached after an elapsed time of 10 days and correspondingly there is still a net loss of plasma from the ionosphere to the magnetosphere at that time. This slow recovery of the H⁺ density and flux patterns, following magnetic storms, indicates that the mid-latitude topside ionosphere may be in a continual dynamic state if the storms occur sufficiently often.     

Relative flow of H+ and O+ ions in the topside ionosphere at mid-latitudes

Theoretical results on the daily variation of O⁺ and H⁺ field-aligned velocities in the topside ionosphere are presented. The results are for an L = 3 magnetic field tube under sunspot minimum conditions at equinox. They come from calculations of time-dependent O⁺ and H⁺ continuity and momentum balance in a magnetic field tube which extends from the lower F2 region to the equatorial plane (Murphy et al., 1976).There are occasions when ion counterstreaming occurs, with the O⁺ velocity upward and H⁺ velocity downward. The conditions causing this counterstreaming are described: the H⁺ layer is descending whilst O⁺ is supplied from below either to increase the O⁺ concentration at fixed heights or to replace O⁺ ions lost by charge exchange with neutral H. It is suggested that the results of observations at Arecibo by Vickrey et al. (1976) of O⁺ and H⁺ concentrations and counterstreaming velocities are significantly affected by $\text{E}\text{×}\text{B}$ drift.