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.     

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.     

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.     

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.     

Thermal ion flows in the topside auroral ionosphere and the effects of low-altitude,transverse acceleration

Topside ionospheric profiles are used to study the upward field-aligned flow of thermal O⁺ at high latitudes. On the majority of the field lines outside the plasmasphere, the mean flux is approximately equal to the mean polar wind measured by spacecraft at greater altitudes. This is consistent with the theory of thermal light ion escape supported, via charge exchange, by upward O⁺ flow at lower heights. Events of larger O⁺ flow are detected at auroral latitudes and their occurrence is found to agree with that of transversely accelerated ions within the topside ionosphere and the magnetosphere. The effects of low altitude heating of O⁺ by oxygen cyclotron waves, driven by downward field-aligned currents, are considered as a possible common cause of these two types of event.     

Temperatures in the polar wind

The thermal structure of the plasma in the polar wind is examined. With O⁺H⁺ Joule heating as the mechanism for heating the plasma, it is found that O⁺ and H⁺ temperatures are significantly greater than the electron temperature. With the adopted input parameters the O⁺H⁺ temperature difference is relatively small.     

A beam/plasma interaction in the high-altitude auroral ionosphere

Ambient thermal electrons are found to be heated to temperatures as high as 10⁵ K by the passage of a field-aligned beam of suprathermal electrons through the ionosphere at altitudes over 660 km. These secondary electrons will increase the proportion of 630 nm emission, caused by the primary electron precipitation, and change the secondary electron spectrum observed at lower altitudes from that expected on the basis of atmospheric collisions alone.     

Ionospheric warming by neutral winds

The effect of frictional heating by means of neutral winds on the ion and electron temperature in the undisturbed ionosphere is studied theoretically by solving a system of basic ionospheric and atmospheric equations. The study shows that both the electron and ion temperatures are increased in the night-time ionosphere through friction. In the region between 150 and 200 km T_i may exceed T₆ by as much as 130°. The increase of T_i due to friction amounts to about 100–200°, depending on the atmospheric model employed in calculating the neutral wind velocity. It is illustrated that frictional heating may be very important for the determination of the neutral temperature from measured ion temperature values.     

A comparison of the temperature and density structure in high and low speed thermal proton flows

The continuity, momentum and energy hydrodynamic equations for an H⁺-O⁺ topside ionosphere have been solved self-consistently for steady state conditions similar to those found outside the plasmasphere. Results are given for undisturbed and trough conditions with a range of H⁺ outflow velocities yielding subsonic and supersonic flow. In the formulation of the equations, account was taken of the velocity dependence of ion-neutral, ion-ion and ion-electron collision frequencies. In addition, parallel stress and the nonlinear acceleration term were retained in the H⁺ momentum equation. Results computed from this model show that, as a result of Joule (frictional) heating, the H⁺ temperature rises with increasing outflow velocity in the subsonic flow regime, reaching a maximum value of about 4000 K. For supersonic flow other terms in the H⁺ momentum equation become important and alter the H⁺ velocity profile such that convection becomes a heat sink in the 1000–1500 km altitude range. This, together with the reduced Joule heating resulting from the high-speed velocity dependence of the H⁺ collision frequencies, results in a decrease in the H⁺ temperature as the outflow velocity increases. However, for all outward flows the H⁺ temperature remains substantially greater than the O⁺ temperature. With identical upper boundary velocities, the H⁺ flow velocity is higher at low altitudes for trough conditions compared with non-trough conditions, but the H⁺ temperature in the trough is lower. The form of the H⁺ density profiles for supersonic flow does not in general differ greatly from those obtained with wholly subsonic flow conditions.     

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.     

Neutral temperatures and emission height changes in an E-region aurora

In this study a method is outlined which is capable of giving neutral temperatures and height changes in the aurora when the molecular emissions originate from the E-region.Absolute spectrometric measurements of N₂⁺ 1NG and O₂⁺ 1NG bands and the auroral green line are performed in a nightside aurora. Rotational temperatures and band intensities are deduced by a least-squares fit of synthetic spectra to observations. There is a close correlation between the variations in rotational temperatures and the relative intensity ratio of N₂⁺ 1NG(0,3) and O₂⁺ 1NG(1,0) bands. The change in the relative intensity ratio is similar to the intensity variation predicted by the changing N₂ and O₂ densities from 120 to 150 km, obtained from the MSIS 83 model atmosphere, and the derived neutral temperature variations are consistent with a similar change in emission height of the aurora. Therefore the changing temperature is most likely due to a changing emission height of the aurora, and no local heating can be inferred.     

Localized ionization patches in the nighttime ionosphere of Mars and their electrodynamic consequences

Using an electron transport model, we calculate the electron density of the electron impact-produced nighttime ionosphere of Mars and its spatial structure. As input we use Mars Global Surveyor electron measurements, including an interval when accelerated electrons were observed. Our calculations show that regions of enhanced ionization are localized and occur near magnetic cusps. Horizontal gradients in the calculated ionospheric electron density on the night side of Mars can exceed 10⁴ cm⁻³ over a distance of a few tens of km; the largest gradients produced by the model are over 600 cm⁻³ km⁻¹. Such large gradients in the plasma density have several important consequences. These large pressure gradients will lead to localized plasma transport perpendicular to the ambient magnetic field which will generate horizontal currents and electric fields. We calculate the magnitude of these currents to be up to 10 nA/m². Additionally, transport of ionospheric plasma by neutral winds, which vary in strength and direction as a function of local time and season, can generate large (up to 1000 nA/m²) and spatially structured horizontal currents where the ions are collisionally coupled to the neutral atmosphere while electrons are not. These currents may contribute to localized Joule heating. In addition, closure of the horizontal currents and electric fields may require the presence of vertical, field-aligned currents and fields which may play a role in high altitude acceleration processes.     

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.     

Vibrational and rotational cooling of electrons by water vapor

The cooling of electrons by vibrational and rotational excitation of water molecules plays an important role in the thermal balance of electrons in cometary ionospheres. The energy loss function for rotational excitation and de-excitation of H₂O by electron impact is calculated theoretically. The rotational cooling rate is calculated using this loss function for a wide range of electron and neutral temperatures. The vibrational cooling rate is calculated using measured values of electron impact vibrational excitation cross sections. Analytical formulae are provided for some of the cooling rates. The interaction of ions with H₂O molecules is also discussed and a formula is suggested for the momentum transfer collision frequency.     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

The problem of hydrodynamic response of the solar chromosphere on impulsive heating by energetic electrons is discussed. All basic physical processes are considered in a one-dimensional approximation, due to presence of a strong magnetic field. The calculations are performed for the heating of the chromosphere by electrons having a power-law energetic spectrum. In the upper chromosphere the electron temperature rises rapidly to values of order 10⁷ K. The ion temperature is more than the order of magnitude less than the temperature of electrons. The heated high-temperature chromospheric plasma expands into corona with a velocity up to 1500 km s^–1. In more dense layers, the fast re-emission of supplied energy takes place. This process gives rise to short-lived EUV flash. Just below the flare transition layer the thermal instability produces cold plasma condensation which moves downward at a velocity exceeding the sonic one in the quiet chromosphere.     

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.     

Winter anomalous D-region over Sardinia (40°N)

A simplified D-region model consisting of O₂⁺, NO⁺ and their respective cluster ions grouped as Z_o2⁺ and Z_NO⁺ is used to reproduce the available rocket data on positive ion relative composition and effective clustering rates for the height range 70–90 km. The results of this analysis for a winter anomalous day (Sardinia, 40°N) are in good agreement with the presently known ideas on NO densities, O₂⁺ production rates, mesospheric temperature, negative ion to electron density ratio and effective loss coefficient for electrons. Mesospheric nitric oxide density and temperature profiles from this study are in excellent agreement with the findings of Zbinden et al. (1975) and Hidalgo (1977) for the anomalous day at Sardinia.     

II. Combined numerical model of ion and neutral composition above 120 km

A coupled neutral-ionic photochemical model has been used to interpret the ionic composition of the Venusian dayside ionosphere measured by the orbiter retarding potential analyser (ORPA) experiment on board the NASA Pioneer-Venus orbiter spacecraft. The electron and ion temperatures also measured by the ORPA are used for calculating the plasma-diffusion coefficients and scale heights for ions. The neutral temperature profiles and the densities of neutral constituents, particularly CO₂ and O, play key roles in the determination of the height profiles of the ionic constituents. All these quantities vary substantially in the Venusian thermosphere near the terminator; the models presented are representatives of the solar zenith angle ～65°. The predicted O₂⁺ densities below ～200km agree particularly well with observations by the ORPA, but the model values are significantly less than those measured by the orbiter ion mass spectrometer (OIMS). Models predict much smaller densities than observed values for all molecular ions above ～200km. The reason for the turn-up trend of the concentration gradient of molecular ions observed at these heights by both ORPA and OIMS is unknown. One of the models can predict O⁺ ion densities above ～200km compatible with observations, if an effective vertical escape flux (φ10⁸cm^?2sec^?1) is assumed at the ionopause. The neutral air density required to explain the observed ion composition is about 1.4 times larger than the values measured by the orbiter neutral mass spectrometer (ONMS).     

The slab thickness of the mid-latitude ionosphere

The thickness of the peak of the ionosphere depends primarily on the temperature T _n of the neutral gas, and corresponds approximately to an α-Chapman layer at a temperature of 0.87T _n. The overall slab thickness, as given by Faraday rotation measurements, is then τ =0.22 _n + 7km. Expansion of the topside ionosphere, and changes in the E-andFl-regions increase τ by about 20 km during the day in summer. Near solar minimum τ is increased by a lowering of the O ⁺/H ⁺ transition height; if the neutral temperature T _n is estimated, this height can be obtained from observed values of τ.Hourly values of slab thickness were determined over a period of 6 yr at 34°S and 42°S. Near solar maximum the night-time values were about 260 km in all seasons. The corresponding neutral temperatures agree with satellite drag values; they show a semiannual variation of 14 per cent and a seasonal change of 5 per cent. Daytime values of τ were about 230 km in winter and 320 km in summer, implying a seasonal change of 30 per cent in T _n. Temperatures increase steadily throughout the day in all seasons, with a rapid post-sunset cooling in summer. Downwards movements produce a large peak in τ at 0600 hr in winter. A large upwards flux, equal to about 40 per cent of the maximum (limiting) value, reduces τ for several hours after sunrise in winter. The slab thickness increases near solar minimum showing a reduction of the O ⁺/H ⁺ transition height to about 700 km in summer and 500 km in winter.