Whistlers as a diagnostic technique in the lower ionosphere

We have taken a plasma model of ionosphere which is quite different from the earlier model employed by several workers to study the whistler as a diagnostic technique in the ionosphere. In contrast to the earlier model, we have considered an ionosphere that includes negative ionic species and due to which the mathematical technique loses the basic assumptions chosen earlier to derive the group travel time. We have shown that the negative ion has a significant role and without its contribution, the method to diagnose the ionospheric parameters may lead to an error. We have discussed also how to uset()= ₀ ^h dh/v _g as a diagnostic tool in determining the ionospheric parameters.     

Viscous flow properties in the transport of solar wind momentum to the Venus upper ionosphere

A comparative study of the viscous transport of solar wind momentum to the upper layers of the Venus ionosphere with that occurring within the trans-terminator flow leads to estimates of the ratio of the viscosity coefficients that are applicable to both cases. Support for viscous forces between the solar wind and the ionospheric plasma in the trans-terminator flow derives from the momentum flux balance between the momentum flux in the latter flow and the deficiency of solar wind momentum along the flanks of the ionosheath. By comparing the relative width of the viscous boundary layer in the Venus ionosheath and the width of the trans-terminator flow we find that the transport of momentum within the upper ionosphere proceeds at a rate similar to that at which momentum is delivered to the upper ionosphere from the solar wind. Comparable values are obtained for the viscosity coefficient of the solar wind that streams over the ionosphere and that implied from momentum transport within the ionospheric trans-terminator flow. It is further suggested that despite the different nature of the processes that give place to the viscous transport of the solar wind momentum to the upper ionosphere (wave-particle interactions) and those responsible for its distribution within the ionosphere (through coulombian collisions) there is a similar response in the behavior of both plasmas to momentum transport. Calculations show that with comparable values of the viscosity coefficient in the ionosheath and in the upper ionospheric plasma the mean free path suitable to wave-particle interactions in the ionosheath is of the same order of magnitude as the mean free path of the planetary O⁺ ions that interact through coulombian collisions in the upper ionosphere. The effects of this similarity are considered in the discussion.     

Response of peak electron densities in the martian ionosphere to day-to-day changes in solar flux due to solar rotation

Photochemical Chapman theory predicts that the square of peak electron density, N_m, in the dayside ionosphere of Mars is proportional to the cosine of solar zenith angle. We use Mars Global Surveyor Radio Science profiles of electron density to demonstrate that this relationship is generally satisfied and that positive or negative residuals between observed and predicted values of are caused by periods of relatively high or low solar flux, respectively.Understanding the response of the martian ionosphere to changes in solar flux requires simultaneous observations of the martian ionosphere and of solar flux at Mars, but solar flux measurements are only available at Earth. Since the Sun's output varies both in time and with solar latitude and longitude, solar flux at Mars is not simply related to solar flux at Earth by an inverse-square law. We hypothesize that, when corrected for differing distances from the Sun, solar fluxes at Mars and Earth are identical when shifted in time by the interval necessary for the Sun to rotate through the Earth–Sun–Mars angle.We perform four case studies that quantitatively compare time series of N_m at Mars to time series of solar flux at Earth and find that our hypothesis is satisfied in the three of them that used ionospheric data from the northern hemisphere. We define a solar flux proxy at Mars based upon the E_10.7 proxy for solar flux at Earth and use our best case study to derive an equation that relates N_m to this proxy. We discuss how the ionosphere of Mars can be used to infer the presence of solar active regions not facing the Earth.Our fourth case study uses ionospheric observations from the southern hemisphere at latitudes where there are strong crustal magnetic anomalies. These profiles do not have Chapman-like shapes, unlike those of the other three case studies. We split this set of measurements into two subsets, corresponding to whether or not they were made at longitudes with strong crustal magnetic anomalies. Neither subset shows N_m responding to changes in solar flux in the manner that we observe in the three other case studies.We find many similarities in ionospheric responses to short-term and long-term changes in solar flux for Venus, Earth, and Mars. We consider the implications of our results for different parametric equations that have been published describing this response.     

Ionospheric Day-to-Day Variability Around the Whole Heliosphere Interval in 2008

Ionospheric F2 peak electron densities (NmF2) measured at ten ionosonde stations have been analyzed to investigate ionospheric day-to-day variability around the Whole Heliosphere Interval (WHI) in 2008 (Day of Year (DOY) 50?–?140). The ionosonde data showed that there was significant global day-to-day variability in NmF2. This variability had 5-, 7-, 9-, 11-, 13.5-, and 16?–?21-day periodicities. At middle latitudes, the ionosphere appeared to respond directly to the solar-wind and interplanetary-magnetic-field (IMF) induced geomagnetic-activity forcing, with the day-to-day variability having the same periods as those in the solar-wind/IMF and geomagnetic activity. At the geomagnetic Equator, the ionosphere had a strong 7-day periodicity, corresponding to the same periodicity in the IMF B _z component. In the equatorial anomaly region, the ionosphere showed more complicated day-to-day variability, dominated by the 9-day periodicity. In addition, there were also periodicities of 11 days and 16?–?21 days in the ionosonde data at some stations. The ionosonde data were compared with the Coupled Magnetosphere Ionosphere Thermosphere (CMIT) simulations that were driven by the observed solar-wind and IMF data during the WHI. The CMIT simulations showed similar ionospheric daily variability seen in the data. They captured the positive and negative responses of the ionosphere at middle latitudes during the first corotating interaction region (CIR) event in the WHI. The response of the model to the second CIR event, however, was relatively weak.     

Cavitation by Nonlinear Interaction Between Inertial Alfvén Waves and Magnetosonic Waves in Low Beta Plasmas

This paper presents the model equations governing the nonlinear interaction between dispersive Alfvén wave (DAW) and magnetosonic wave in the low-β plasmas (β≪m _e/m _i; known as inertial Alfvén waves (IAWs); here \upbeta = 8pn₀T /B₀²\upbeta = 8\pi n_{0}T /B_{0}^{2} is thermal to magnetic pressure, n ₀ is unperturbed plasma number density, T(=T _e≈T _i) represents the plasma temperature, and m _e(m _i) is the mass of electron (ion)). This nonlinear dynamical system may be considered as the modified Zakharov system of equations (MZSE). These model equations are solved numerically by using a pseudo-spectral method to study the nonlinear evolution of density cavities driven by IAW. We observed the nonlinear evolution of IAW magnetic field structures having chaotic behavior accompanied by density cavities associated with the magnetosonic wave. The relevance of these investigations to low-β plasmas in solar corona and auroral ionospheric plasmas has been pointed out. For the auroral ionosphere, we observed the density fluctuations of ∼ 0.07n ₀, consistent with the FAST observation reported by Chaston et al. (Phys. Scr. T84, 64, 2000). The heating of the solar corona observed by Yohkoh and SOHO may be produced by the coupling of IAW and magnetosonic wave via filamentation process as discussed here.     

Ducted propagation of hydromagnetic waves in the F2 layer

Calculations of the properties of the ionospheric duct centered at the F₂ layer are carried out with a view to investigating the ducted propagation of Pc1 micropulsations in directions out of the geomagnetic meridian plane. For a horizontally uniform ionosphere, duct properties are found to be essentially the same in all horizontal directions. Propagation characteristics of ducted waves, however, vary according to ionospheric and sunspot conditions. In practice, therefore, it is expected that horizontal propagation over a large recording network is not isotropic because of the diurnal changes in the ionosphere.     

A comparison study between the newly-born ion effect and the thermal effect on the whistlers in the ionosphere

We have considered an ionospheric plasma model that includes the thermal effect along with the newly born ionic effect and derived a group travel time for the low-frequency whistlers with a view to employing it as a diagnostic tool in the ionosphere. The mathematical development shows that the thermal effect contribution varies with ( _i – )_–7/2 whereas that of the newly born ionic effect varies with _i – )_–5/2. Both the effects are discussed separately. It is concluded that the effects are reasonably countable in the ionosphere. The investigations finally conclude that both the effects should be taken into the whistler waves, otherwise the method might cause a discrepancy in the results, which could affect their accuracy.     

Small perturbations in flat galaxies

The aim of this series of papers is to develop straightforward methods of computing the response of flat galaxies to small perturbations. This Paper I considers steady state problems; Paper II considers time varying perturbations and the effects of resonances; and Paper III applies the methods developed in Papers I and II to a numerical study of the stability of flat galaxies.The general approach is to study the dynamics of each individual orbit. The orbits are described by their apocentric and pericentric radii,r _a andr _p , and the distribution function of an equilibrium model is a function ofr _a andr _p . The mass density and potential corresponding to a distribution function is found by means of an expansion in Hankel-Laguerre functions; the coefficients of the expansion being found by taking moments of the mass density of the individual orbits. This leads to a simple method of constructing equilibrium models.The response to a small perturbation is found by seeking the response of each orbit. When the perturbations are axisymmetric and slowly varying, the response can be easily found using adiabatic invariants. The potential is expanded in a series of Hankel-Laguerre functions, and the response operator becomes a discrete matrix. The condition that the model is stable against adiabatic radial perturbations is that the largest eigenvalue of the response matrix should be less than one.An analytic approximation to the response matrix is derived, and applied to estimate the eccentricity needed for stability against local perturbations.     

A possible current system associated with the Sqp variation

It is suggested that the quiet day daily magnetic variation in the polar cap region, S_q^p, results partly from the short-circuit effect of the magnetotail current by the polar ionosphere. This implies that there is an inward field-aligned current from the dawnside magnetopause to the forenoon sector of the auroral oval (positively charged) and an outward field-aligned current to the duskside magnetopause from the afternoon sector of the oval (negatively charged), together with the ionospheric (Pedersen and Hall) currents. The distribution of the magnetic field vectors of both combined current systems agrees with the observed S_q^pvector distribution. The space charges provide an electric field distribution which is similar to that which has been observed by polar orbiting satellites.     

The G-dwarf problem in the solar neighbourhood: a Lagrangian picture. II

The current paper investigates how the empirical, G-dwarf metallicity distribution constrains simple, comoving models of chemical evolution. In doing this, the application of the models to a data sample, performed in a previous paper, is refined and extended. The key idea is that (i) different star formation rates with different mass spectra take place in different phases of evolution, i.e. contraction and equilibrium, and (ii) disk formation begins at a time t = T_d and ends at t = T_c, which marks the transition from contraction to equilibrium. In this view, the lowest-metallicity point of the empirical, differential distribution, consistent with a linear fit, is related to the beginning of disk formation, and an apparent discontinuity point to the transition from contraction to equilibrium. In addition, different linear fits hold on the left (early distribution) and on the right (late distribution) of the discontinuity point. Models consistent with the empirical, G-dwarf metallicity distribution are related to linear fits on the early and late side. Homologous solutions during the equilibrium phase are analysed in detail with respect to changes in T_c and T_a, the age of the Galaxy. Then we are left with a single free parameter which is relevant to the chemical evolution, i.e. the mass spectrum exponent during the equilibrium phase. The allowed values for the other parameters, thought as a function of the above mentioned one, are plotted for each case. A Salpeter mass spectrum exponent, p = −2.35, is ruled out by the theoretical, lower stellar mass limit, contrary to a Scalo mass spectrum exponent, p = −2.90, in contrast with previous literature. The reasons for this discrepancy are discussed. Our results are marginally consistent with a same initial mass function during the contraction and equilibrium phase, but in this case the disk mass fraction is of the is same order, or less, than the halo mass fraction. It is also investigated how the empirical age-metallicity relation constrains the duration of the contraction phase, for a reasonable upper limit of T_a. Keeping in mind that the empirical, G-dwarf metallicity distribution has not been corrected for the large cosmic scatter shown by the empirical, age-metallicity relation, we find a duration of disk formation, T_c — T_d = 1.07–1.5 Gyr, by a factor 3–5 less than it is found by use of simple infall models. The reasons of this difference are explained. The idea of a massive, white dwarf halo, which seems to be indicated by microlensing experiments, is ruled out by the empirical, G-dwarf metallicity distribution, in the light of the current model and provided the solar neighbourhood is a typical region of the Galaxy. More refined models involving e.g., the relax of instantaneous recycling would change our results, but the trend is expected to be only slightly altered.     

Ionosphere-plasmasheet field-aligned currents and parallel electric fields

Two kinetic models for the auroral topside ionosphere are compared. The collisionless plasma distributed along an auroral magnetic field line behaves like a non-Ohmic conducting medium with highly non-linear characteristic curves relating the parallel current density to the potential difference between the cold ionosphere and the hot plasmasheet region. The (zero-electric current) potential difference, required to balance the current carried by the precipitating plasmasheet particles and the current transported by the outflowing ionospheric particles, depends on the ratio n_ps.e/n_th.e and T_ps.e/T_th.e of the plasmasheet and ionospheric electron densities and temperatures. When in the E-region the magnetic field lines are interconnected by a high conductivity plasma the resulting field-aligned currents driven by the magnetospheric potential distribution are limited by the integrated Pedersen conductivity of the ionospheric layers. These currents are not related to the parallel electric field intensity as they would be in Ohmic materials. The parallel electric field intensity is necessarily determined by the local quasi-neutrality of the plasma.     

Dependence of the aerosol component of optical thickness and the relative concentration of methane on depth in atmospheres of giant planets

Based on the data on a spectral dependence of the geometric albedo of giant planet discs, we obtained depth variations in the optical thickness τ _a of the aerosol component and relative concentration γ of methane (Uranium, Neptune) lnτ _a = −0.720 + 1.507Δlnp (for −2.2085 ≤ lnp ≤ −1.0018), lnτ _a = +1.224 + 1.160Δlnp (for −1.0018 ≤ lnp ≤ −0.0595), lnτ _a = +2.318 + 0.192Δlnp (for −0.0595 ≤ lnp), γ = 0.0027 for Jupiter; lnτ _a = −0.846 + 1.598Δlnp (for −3.3619 ≤ lnp ≤ −2.0575), lnτ _a = +1.238 + 1.342Δlnp (for −2.0575 ≤ lnp ≤ −1.2074), lnτ _a = +2.379 + 0.722 (for −1.2074 ≤ lnp ≤ −0.6501), lnτ _a = +2.781 + 0.326Δlnp (for 0.6501 ≤ lnp), γ = 0.0027 for Saturn; lnτ _a = −2.694 + 0.087Δlnp (for +0.3685 ≤ lnp ≤ +1.2314), lnτ _a = −2.619 + 7.341Δlnp (for +1.2314 ≤ lnp ≤ +1.7556), lnτ _a = +1.229 + 0.956Δlnp (for +1.7556 ≤ lnp) for Uranium; lnτ _a = −1.861 + 1.248Δlnp (for +0.3204 ≤ lnp ≤ +0.9051), lnτ _a = −1.131 + 0.347Δlnp (for +0.9051 ≤ lnp) for Neptune; depth-averaged relative methane concentration lnγ = −9.982 + 2.676Δlnp(0.3584 ≤ lnp ≤ 1.5445); ln γ = −9.738 + 2.561Δlnp(0.3237 ≤ lnp ≤ 1.6156) and γ = 0.00382(lnp ≥ 1.6156); 0.00554(lnp ≥ 1.6156) for Uranium and Neptune, respectively (p is in bar).     

Dynamical portrait of the Lixiaohua asteroid family

In this paper we present a comprehensive analysis of the dynamics in the region of the (3556) Lixiaohua asteroid family. The family lies in a particularly interesting region of the phase space, crossed by several two-body and three-body mean motion resonances. Also, members of this family can have close encounters with large asteroids, such as Ceres. We have identified the mean motion resonances which contribute to the long-term dynamical evolution of the family and our results confirm that the members of this family can be classified into a number of groups, exhibiting different dynamical behavior. We show for the first time that in the Lixiaohua region, apart from the chaotic diffusion in proper eccentricity and inclination (e _p and I _p ), there is at least one extended chaotic zone where several resonances overlap, thus giving rise to chaotic diffusion in proper semi-major axis (a _p ) as well. Using a code of Monte Carlo type, we simulate the evolution of the family, according to the model which combines the chaotic diffusion (in a _p , e _p and I _p ), Yarkovsky/YORP thermal effect and random walk in a _p due to the close encounters with massive asteroids. These simulations show that all these effects should be taken into account in order to accurately explain the observed distribution of family members in the space of proper elements, although a “minimal” model that accounts for chaotic diffusion in (e _p , I _p ), Yarkovsky-induced drift in a _p and random walk in a _p due to the close encounters with the most massive asteroids is enough to grossly characterize the shape of the family.     

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.     

The effect of realistic conductivities on the high-latitude neutral thermospheric circulation

The dynamics of the high latitude thermosphere are dominated by the ion circulation pattern driven by magnetospheric convection. The reaction of the neutral thermosphere is influenced by both the magnitude of the ion convection velocity and by the conductivity of the thermosphere. Using a threedimensional, time-dependent, thermospheric, neutral model together with different ionospheric models, the effect of changes in conductivity can be assessed. The ion density is described by two models: the first is the empirical model of Chiu (1975) appropriate for very quiet geomagnetic conditions, and the second is a modified version of the theoretical model of Quegan et al. (1982). The differences in the neutral circulation resulting from the use of these two ionospheric models emphasizes the need for realistic high latitude conductivities when attempting to model average or disturbed geomagnetic conditions, and a requirement that models should couple realistically the ionosphere and the neutral thermosphere. An attempt is made to qualitatively interpret some of the features of the neutral circulation produced at high latitudes by magnetospheric processes.     

A model of the electron and ion temperatures in the ionosphere

A model (empirical) of the electron and ion temperatures (T_eT_i) is presented in the altitude interval 50–4000 km as a function of time (diurnal, annual), space (position, altitude) and solar flux (F_10.7). Using observations of six satellites (AE-C, AE-D, AE-E, ISIS-1, ISIS-2, OGO-6), five incoherent scatter stations (Arecibo, Chatanika, Jicamarca, Millstone Hill, St Santin) and rocket measurements, this model describes the global gross features of the ionosphere during quiet geophysical conditions (K_p⩽3). The numerical analysis is based on spectral decomposition; the horizontal structure is represented by spherical harmonies and Fourier series, and the vertical structure by spline functions. The electron temperature is, in general, very similar to the ion temperature below ∼90 km. Up to approx. 1500 km, the electron temperature is, on an average, distinctly higher than the ion temperature. Above ∼2000 km, however, the ion temperature is quickly catching up and attains somewhat below 4000 km the same magnitude as the electron temperature.     

A new theoretical approach to the modelling of toroidal Pc5 pulsations

A model is developed to represent a toroidal mode of Pc5 geomagnetic pulsations. It is shown that this model is consistent in its predictions, such as the latitude profiles of amplitude and phase and their dependence on the height integrated Pedersen conductivity, Σ_p, with those of Walker's (1980) theory. It is also shown that this theory is relatively easily capable of accommodating (i) a variety of field line plasma mass density distributions, (ii) a variety of external excitation schemes, (iii) unequal Σ_p's at each end of the field lines and (iv) non-dipolar geomagnetic fields. The theory yields the transient as well as the steady state response, an important feature permitting application to short-lived events or to those for which the generator is amplitude modulated. It is shown, for instance, that the amplitude-latitude profile varies during the transient. It is also shown that the steady state latitude profiles of amplitude and phase are the dual of those observed as a function of frequency when the excitation frequency is scanned through a resonance. A more realistic steady state energy flow from a generator along the field lines to the ionosphere is inherent in this theory compared with that from the mode to the ionosphere which is inherent in Walker's theory.     

Increase in the response of the Earth's atmosphere to the sunspot cycle with height above sea level

The average, longterm behaviour of many parameters P of the Earth's atmosphere and ionosphere depends on the solar activity cycle. In many cases it can be roughly described by a linear approximation of the form P = P ₀(1 + kR), where for example, P is electron density of the ionosphere or stratospheric temperature, and so on; R is an average sunspot number; k indirectly gives the response of particular constituents of the Earth's atmosphere above the tropopause to the corresponding region(s) of the solar wave spectrum. It is shown that this response coefficient k considerably depends on season, and also slightly on the hemisphere considered and on geographic latitude, and that it increases by orders of magnitude with height above the sea level. The coefficient k is greatest for the F region of the ionosphere; it is still significant for stratospheric temperatures, but mainly during winter, and it becomes slightly negative for tropospheric temperatures.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Field-aligned and ionospheric currents

Zmuda and Armstrong (1974) showed that the field-aligned currents consist of two pairs; one is located in the morning sector and the other in the evening sector. Our analysis of magnetic records from the TRIAD satellite suggests that in each pair the poleward field-aligned current is more intense than the equatorward current, a typical ratio being 2:1. This difference has a fundamental importance in understanding the coupling between the magnetosphere and the ionosphere. We demonstrate this importance by computing the ionospheric current distribution by solving the continuity equation $\text{▽ .}\text{I}\text{= j}{}_{\mathrm{\parallel }}$ using the “observed” distribution of j_∥ for several models of the ionosphere with a high conductive annular ring (simulating the auroral oval).It is shown that the actual field-aligned and ionospheric current system is neither a simple Birkeland type, Boström type nor Zmuda-Armstrong type, but is a complicated combination of them. The relative importance among them varies considerably, depending on the conductivity distribution, the location of the peak of the field-aligned currents, etc. Further, it is found that the north-south segment of ionospheric current which connects the pair of the field-aligned currents in the morning sector does not close in the same meridian and has a large westward deflection. Thus, it has an appreciable contribution to the westward electrojet. One of the model calculations shows that the entire north-south closure current contributes to the westward electrojet.