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.     

Propagation of Hydrogentic waves in the upper F2-region>

The theory of hydromagnetic-wave in the upper F2-region, in which electrons are in a transitional regime from collisional to collisionless conditions and ions are in a collisionless state, is examined. Derivation of the governing equations is based on the fact that the isotropic electrons are fluid-like, and the anisotropic ions follow kinetic equations modified by ion-electron collisions. Magneto-acoustic waves of a period of 0.2–10 sec are dissipated by ion Landau damping and electron thermal conduction and viscosity. Numerical solutions under ionospheric conditions show that the dissipation of hydromagnetic waves is insufficient to modify the large scale heating of the ionosphere.     

Turbulent transport and heating in the auroral plasma of the topside ionosphere

Using plasma parameters from a typical stormtime ionospheric energy balance model, we have investigated the effects of plasma turbulence on the auroral magnetoplasma. The turbulence is assumed to be comprised of electrostatic ion cyclotron waves. These waves have been driven to a nonthermal level by a geomagnetic field-aligned, current-driven instability. The evolution of this instability is shown to proceed in two stages and indicates an anomalous increase in field-aligned electrical resistivity and cross-field ion thermal conductivity as well as a decrease in electron thermal conductivity along the geomagnetic field. In addition, this turbulence heats ions perpendicular to the geomagnetic field and hence leads to a significant ion temperature anisotropy.     

Boltzmann-Fokker-Planck model for the electron distribution function in the Earth's ionosphere

Using Boltzmann-Fokker-Planck methods and the diffusion approximation, we derive coupled non-linear equations for the first two angular moments of the electron distribution function in the Earth's ionosphere. The theory includes a phenomenological treatment of photionization of the neutral species by an externally produced photon flux; electron-ion recombination; electronneutral particle attachment; elastic, excitation, deexcitation, and ionizing electron-neutral particle collisions; and elastic electron-electron and electron-ion collisions. At high and low energies, we obtain approximate analytic solutions for the steady-state electron distribution function. Under certain conditions we also obtain the standard continuous slowing-down formulae for the steady-state electron distribution function in the diffusion approximation.     

The upper atmosphere as a regulator of subauroral red arcs

The mechanisms for producing a subauroral red arc (SARARC) are studied by solving a system of basic ionospheric and atmospheric equations. It is shown that many of the observed features of a SARARC can be explained within the framework of the two processes generally responsible for the ionospheric behavior during a magnetic storm: these are (1) energy conduction from the magnetosphere to the ionosphere and (2) the changes in neutral composition of the lower atmosphere caused by the increase in turbulent mixing. Both the processes trigger a complex chain of events which ultimately results in the redistribution of both the charged and neutral particles, an increase in the electron, ion, and neutral temperatures, and a decrease in the electron density in the altitude region near the F2 peak. It is shown that both the occurrence and the emission intensity of a SARARC are regulated by the neutral atmosphere, even though conduction of the thermal energy from the magnetosphere to the ionosphere provides the excitation energy fo the optical remission. Recent satellite measurements of the ionospheric parameters have confirmed the validity of these findings and have provided grounds for rejecting several other theories which have been proposed in the literature.     

Solutions to bi-Maxwellian transport equations for SAR-arc conditions

We have compared solutions obtained from the bi-Maxwellian based 16-moment transport equations with those obtained from the Maxwellian based 13-moment transport equations for conditions leading to the steady state, subsonic flow of a fully-ionized electron-proton plasma along geomagnetic field lines in the vicinity of the plasmapause. The bi-Maxwellian based equations can account for large temperature anisotropies and the flow of both parallel and perpendicular thermal energy, while the Maxwellian based equations account for small temperature anisotropies and only the total heat flow. Our comparison indicates that for Stable Auroral Red arc (SAR-arc) conditions leading to strong field-aligned heat flows (temperatures of 8000 K and temperature gradients of4K. km⁻¹ at 1500 km), the bi-Maxwellian based equations predict a different thermal structure in the topside ionosphere than the less rigorous Maxwellian based equations. In particular, the bi-Maxwellian based equations predict proton and electron temperature anisotropies with T > T, while the Maxwellian based equations predict the opposite behavior for the same boundary conditions. This difference is related to the way in which the temperature anisotropies and heat flows are treated in the two formulations. For the bi-Maxwellian based equations, the inclusion of separate heat flows for parallel and perpendicular thermal energy allows for the development of a pronounced tail in both the electron and proton distribution functions, which leads to temperature anisotropies with T > T. For the Maxwellian based equations, on the other hand, the tail development is restricted because only the total heat flow is considered. Consequently, as the heat flows down, the presence of an increasing magnetic field acts to produce an anisotropy with T > T, and this process dominates tail formation for the Maxwellian based equations.     

Analytical Approach to Calculate Quasi-thermal Noise Spectrum in Irregular Plasma

Basic properties of quasi-thermal noise spectrum in irregular plasma have been investigated using an analytical point of view. A simple formula for the plasma frequency splitting effect has been obtained for ionospheric conditions. A passive electric antenna, immersed in a stable plasma, detects the fluctuations of the electric potential due to thermal motion of the ambient particles. Properties of this quasi-thermal noise spectrum in homogeneous plasma are relatively well known and are effectively used for diagnostics of space plasma (Aksenov et al., 1978; Trakhtengerts and Chugunov, 1978; Kellog, 1981; Meyer-Vernet and Perche, 1989). Especially, in the Earth's ionosphere or solar wind plasma, random irregularities of electron density are always present. These irregularities may substantially change properties of these media through electromagnetic radiation and may also modify quasi-thermal noise spectrum, which depends on the effective dielectric permittivity tensor. This tensor is defined as the dielectric permittivity tensor of some imaginary `effective' regular medium in which the field of point source is the same as the mean field in the medium with random irregularities (Ryzhov, Tamoikin and Tatarskii, 1965; Ryzhov 1968). Since the correlation function of electric field fluctuations in random medium may be expressed through the effective dielectric constant tensor (Ryzhov, 1968), it may be used for direct calculation of quasi-thermal noise spectrum. In Zabotin et al. (2000), the Born approximation was used to calculate numerically the effective dielectric permittivity tensor and the modified noise spectrum while we analytically estimate herein the modified noise spectrum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulation of ionosphere-plasmasphere coupling taking into account ion inertia and temperature anisotropy

In this paper we offer a model for the Earth's ionosphere and plasmasphere, allowing for the inertia and anisotropic energy distribution of thermal plasma. A procedure for simultaneous solution of equations of continuity and motion for the O⁺ and H⁺ ions, subject to inertia terms, is described. The model also includes transfer equations for longitudinal and transversal thermal energies. The system of simulating equations and the kinetic equation for superthermal electron spectra are concordantly solved along geomagnetic field lines. Within the framework of the model we developed a study is made of the dynamics of filling of the evacuated plasmaspheric reservoir after a magnetospheric disturbance. It is shown that the filling of the tubes offorce with L ? 3.5 proceeds with supersonic speeds during the first several days and the character of filling differs very much from a diffusion-equilibrium one. The spatio-temporal behavior of electron and ion temperature anisotropy that is formed in the process of filling, is considered. It is found that the value of electron anisotropy can be large. A brief analysis is made of the causes of electron and ion temperature anisotropy.     

Transport equations for aeronomy

In this paper we present results for a general system of transport equations appropriate to a multi-constituent gas mixture. This system includes a continuity, momentum, internal energy, pressure tensor and heat flow equation for each species. The results can be applied to both collision dominated and collisionless plasmas with there being explicit limits derived for the validity of the various expressions. In the limit of very frequent collisions the pressure tensor and heat flow equations give the usual Navier-Stokes results for the viscous stress tensor and heat flow vector. Furthermore, the momentum equation includes thermal diffusion and thermoelectric transport coefficients equivalent to the second approximation of Chapman and Cowling. The basic system of equations has been applied to different regions of the ionosphere and neutral atmosphere. It is found that: (1) The viscous stress tensor and heat flow expressions used in previous studies of the neutral thermosphere may not be appropriate; (2) The transport coefficients normally used for mid-latitude F2-region and topside studies seem to be adequate; (3) The high speed flow of plasma in the polar topside ionosphere is likely to be strongly affected by stresses and heat flow; and (4) E- and F-region ionization at high latitudes is substantially affected by stresses and heat flow.     

Evidences of a distorted electron energy distribution in ionospheric plasma

The energy distribution of thermal electrons in the ionospheric plasma was measured by means of a glass-sealed Langmuir probe. Second derivatives of the v-i curves were obtained electrically by using the second harmonic method. The height of the measurement was from 103 to 360 km.Above 130 km the energy distribution of thermal electrons were Maxwellian enough to evaluate electron temperature. Below 130 km the electrons appeared to consist of two groups of electrons of different temperatures. Because of the bi-Maxwellian energy distribution, the apparent electron temperature obtained from the above method differed from that of an electron temperature probe.     

On the collisional theory of the anisotropic solar wind plasma

The collisional equations for the solar wind assuming steady, spherically symmetric flow and including thermal conduction and an anisotropic proton temperature are analysed in the absence of a heat source function. The equations are cast in a form that involves one dimensionless parameter, effectively equal to the inverse Péclet number for protons, and the small quantity , the square-root of the electron-proton mass ratio. Analytic forms for the proton temperature anisotropy and other flow variables are derived by applying the limit 0, and using asymptotic techniques. It is found that the model based purely on Coulomb collisions predicts values for the proton temperature anisotropy in the vicinity of the Earth that are much smaller than those observed, and that increasing the coronal base temperature serves to decrease the predicted anisotropy still further.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Bianchi type-VI0 conformally invariant scalar fields

An exact solution of Einstein's equations corresponding to the conformally invariant scalar field with tracefree energy-momentum tensor as source is obtained in Bianchi type VI₀ class of metrics. The solution represents a spatially homogeneous but anisotropy universe which admits anisotropic expansions. Some properties of the cosmological model are discussed.     

The linear stability of dilute particulate rings

Irregular structure in planetary rings is often attributed to the intrinsic instabilities of a homogeneous state undergoing Keplerian shear. Previously these have been analysed with simple hydrodynamic models. We instead employ a kinetic theory, in which we solve the linearised moment equations derived in Shu and Stewart 1985 for a dilute ring. This facilitates an examination of velocity anisotropy and non-Newtonian stress, and their effects on the viscous and viscous/gravitational instabilities thought to occur in Saturn's rings. Because we adopt a dilute gas model, the applicability of our results to the actual dense rings of Saturn are significantly curtailled. Nevertheless this study is a necessary preliminary before an attack on the difficult problem of dense ring dynamics. We find the Shu and Stewart formalism admits analytic stability criteria for the viscous overstability, viscous instability, and thermal instability. These criteria are compared with those of a hydrodynamic model incorporating the effective viscosity and cooling function computed from the kinetic steady state. We find the two agree in the ‘hydrodynamic limit’ (i.e., many collisions per orbit) but disagree when collisions are less frequent, when we expect the viscous stress to be increasingly non-Newtonian and the velocity distribution increasingly anisotropic. In particular, hydrodynamics predicts viscous overstability for a larger portion of parameter space. We also numerically solve the linearised equations of the more accurate Goldreich and Tremaine 1978 kinetic model and discover its linear stability to be qualitatively the same as that of Shu and Stewart's. Thus the simple collision operator adopted in the latter would appear to be an adequate approximation for dilute rings, at least in the linear regime.     

Comparative study of Langmuir probe characteristics in different ionospheric conditions

This paper examines the role played by the high energy tail of the electron distribution function on Langmuir probe characteristics. A model is developed to derive the mean energy and the density of the hyperthermal electrons from probe characteristics for two ionospheric rocket flights involving different plasma conditions. The hyperthermal electrons are shown to influence the electron temperature measurement even if they constitute only a small fraction of the total electron concentration. The influence of the geomagnetic field, the collisions and the velocity of the vehicle on the probe data are also examined.     

Comparison of different instantaneous models of electron concentration height profiles at single location

Three different models of electron concentration height profile have been compared to profiles obtained from ionograms at the Warsaw station. The electron density profiles are obtained from ionograms by inversion methods. These models use as an input the standard ionospheric characteristics. Some of the models are intended to compute monthly median profiles. To obtain the instantaneous profile the values of needed parameters are taken from the simultaneously constructed instantaneous maps of ionospheric parameters. For instantaneous maps construction, two techniques are used: the kriging technique with modifications concerning ionospheric behaviour, where deviations of measurements from monthly median maps are used, and a fitting method where median maps are updated with measurements. The comparison is done for the COST 238 PRIME height profile model, a local model based on a modified Rush model, and a model where an artificial neural network technique is aaplied to time series of profiles. The usefulness of the average representative height profile constructed from a set of instantaneous profiles is discussed.     

Collision frequency and transport properties of electrons in the ionosphere

A unified ionospheric electron collision frequency model profile 〈ν_g〉 has been calculated in the height range 50–500 km. The computed profile accounts for the electron collisions with the neutral particles as well as the ions. Experimental values of momentum transfer cross-sections have been used for electron collisions with N₂, O₂ and Ar and theoretical values for N, O, He and H. It is observed that the electron-ion collisions 〈ν_ei〉 dominate over the electron-neutral collisions 〈ν_en〉 above 170 km. However, 〈ν_e?N〉 is of the same order of magnitude as 〈ν_e?O〉 in the height range 170–210 km. Above 360 km 〈ν_e?O〉 becomes more important among the neutrals. The temporal, seasonal and solar epoch variations of 〈ν_ei〉 are also shown. A typical electron collision frequency profile 〈ν_g〉 corresponding to the exospheric temperature of 1100 K has been compared with the available experimental results for D, E and F-regions obtained from different experimental techniques. This profile has been used to determine the electrical, thermal, heat flow and current flow conductivities, the mobility and the diffusivity of electrons. The results so obtained are found to be in good agreement with the earlier results.     

Ionospheric plasma flow past a semi-infinite cylinder

The ionospheric flow regime in which the flow velocity is well above the ambient ion thermal velocity, but far below the ambient electron thermal velocity, is considered. The flow is parallel to the axis of a conducting semi-infinite cylinder and is directed toward the end disk. Taylor's heuristic method is employed to obtain the approximate spatial dependence of the electric potential and the ion density and velocity. An expression is obtained from these parameters for the net current to the end disk.     

Investigation of the force balance in the Titan ionosphere: Cassini T5 flyby model/data comparisons

Cassini’s Titan flyby on 16 April, 2005 (T5) is the only encounter when the two main ionizing sources of the moon’s atmosphere, solar radiation and corotating plasma, align almost anti-parallel. In this paper a single-fluid multi-species 3D MHD model of the magnetospheric plasma interaction for T5 conditions is analyzed. Model results are compared to observations to investigate the ionospheric dynamics at Titan as well as to understand the deviations from a typical solar wind interaction, such as Venus’ interaction with the solar wind. Model results suggest that for the T5 interaction configuration, corotating plasma is the dominant driver determining the global interaction features at high altitudes. In the lower ionosphere below ～1500 km altitude – where the control of the ionospheric composition transfers from dynamic to chemical processes – magnetic and thermal pressure gradients oppose each other locally, complicating the ionospheric dynamics. Model results also imply that the nightside ionosphere – produced only by the impact ionization in the model – does not provide enough thermal pressure to balance the incident plasma dynamic pressure. As a result, the induced magnetic barrier penetrates into the ionosphere by plasma convection down to ～1000 km altitude and by magnetic diffusion below this altitude. Moreover, strong horizontal drag forces due to ion-neutral collisions and comparable drag forces estimated from possible neutral winds in the lower ionosphere below ～1400 km altitude oppose over local regions, implying that the Titan interaction must be treated as a 3D problem. Ion and electron densities calculated from the model generally agree with the Cassini Ion Neutral Mass Spectrometer and Langmuir probe measurements; however, there are significant differences between the calculated and measured magnetic fields. We discuss possible explanations for the discrepancy in the magnetic field predictions.