The effect of finite ionosphere conductivities on axisymmetric toroidal Alfvén wave resonances

Previously developed solutions for pure toroidal mode Alfvén waves with finite ionosphere conductivities are modified to apply both inside and outside the plasmapause.Detailed diagrams are provided to illustrate the effect of realistic ionosphere conductances on the wave-forms. As well as graphs of wave-period, these include: (a) half-wave solutions showing the effect of dipole field distortion and consequent enhancement of ionosphere electric fields; (b) half-wave solutions with low damping that are symmetric and asymmetric about the equatorial plane; (c) highly-damped half-wave and quarter-wave solutions with wave admittance at the ionosphere nearly equal to the ionosphere conductance; (d) a quarter-wave solution with low damping that has a “near-node” of electric field at one ionosphere and an antinode of electric field at the other.     

Toward some new directions in Pc5 pulsation theory—I. Consequences of ionosphere hall current

The Pc5 pulsation model of Rostoker and Lam (1978), which was constructed on the assumption of a non-axisymmetric magnetosphere-ionosphere, is extended to account for the consequence of the ionosphere Hall current. The purpose of the extension is to determine if the more difficult equivalent extension of the hydromagnetic wave theory would be profitable by obtaining some insight into the probable results of such an extension. The new model predicts that the natural resonant frequency is altered by the ionosphere conductivities. This alteration is examined in detail. Another prediction is that the east-west current flow in the ionosphere differs in phase from the north-south current. This phase difference contributes to the polarization properties of the ground-observed pulsations. These results are consequences of the behaviour of the resonant circuit and not that of the signal source. The relationship of this work to that using the traditional approach is discussed.     

Magnetospheric electric fields and protonospheric coupling fluxes inferred from simultaneous phase and group path measurements on whistler-mode signals

A method of measuring the radial component of plasma velocity (or azimuthal electric field) in the equatorial plane of the plasmasphere, and of measuring the flux of plasma between the plasmasphere and the ionosphere is presented. The method uses measured rates of change of phase path and group delay of whistler-mode VLF signals transmitted between geomagnetically conjugate points.Results from four nights are in general agreement with results published by others—equatorial radial velocities of tens of metres per second (azimuthal electrical fields of one or two tenths of a mV/m), fluxes a few times 10¹² m^?2 s^?1-and illustrates the potential and limitations of the method.     

Propagation of VLF emissions in the magnetosphere and the ionosphere

Comparison of the low altitude polar orbiting Injun 5 Satellite data with the ground VLF data has revealed that there is a definite scarcity of VLF/ELF emissions at the ground level compared with the extent to which they are present at or above the auroral altitudes. Reasons for this have been investigated by performing ray path computations for whistler mode VLF propagation in an inhomogeneous and anisotropic medium, such as the magnetosphere and the ionosphere. Based on wave normal computations in the lower ionosphere, it has been found that many of the near-auroral zone VLF/ELF events are frequently either reflected from, or heavily attenuated in, the lower ionosphere. Besides collisional loss, severe attenuation of VLF signals in the lower ionosphere is also caused by the divergence of ray paths from the vertical (spatial attenuation). Cone of wave normal angles for the wave, within which VLF/ ELF signals are permitted to reach the ground, has been established. Wave normals lying outside this transmission cone are reflected from the lower ionosphere and do not find exit to the Earth-ionosphere cavity. Computations for VLF signals produced at auroral zone distances in the equatorial plane of the magnetosphere indicates that these signals are more or less trapped in the magnetosphere at altitudes > 1R_E.     

Magnetic pulsation behaviour in the magnetosphere inferred from whistler mode signals

During a long series of recordings of the Doppler shift of signals from NLK, Seattle, which have propagated in ducts in the whistler mode, a number of occasions have been noted where the duct has been acted on by the electric field of micropulsation events in the Pc4–5 range. Large oscillations are produced in the Doppler shift of the received VLF signal.It is shown that the field line has an antinode of motion in the equatorial plane, and that the Doppler shift is responding almost entirely to the radial component of the duct motion. The latter enables a comparison to be made between the magnetic disturbance in the magnetosphere and that seen on the ground. Some support is given to the prediction of Hughes (1974) and Inoue (1973) that the magnetospheric disturbance vector when seen on the ground is rotated 90° by the currents induced in the ionosphere. Models of the oscillating field line enable an estimate to be made of the azimuthal component of the electric field in the equatorial plane. This is typically $\text{1}\text{mV}\text{m}$. The model also predicts the north-south magnetic field strength of the transverse standing wave at the base of the magnetosphere, and this value may be compared with that seen on the ground. Values of the order 1–2 times the ground H-component or 5–10 times the ground D-component were found.     

Polar magnetic substorms

From the world distribution of geomagnetic disturbance, the connection between the electric current in the ionosphere, the field-aligned current and asymmetric equatorial ringcurrent in the magnetosphere is discussed. The partial ring-current in the afternoon-evening region, whose intensity is closely correlated with the AE-index, usually develops and decays earlier than the symmetric ring-current in the course of magnetic storms. The partial ringcurrent seems to have a direct connection with the positive geomagnetic bay in high latitudes in the evening hours through the ionizing effect of the particles leaking from the partial ringcurrent. The dawn-to-dusk electric field in the magnetospheric tail is transferred to the polar ionosphere, producing there the twin vortex Hall current responsible for polar cap geomagnetic variation. The magnetic effect of the associated Pedersen current in the ionosphere is shown to be small but still worth considering. The electrojet near midnight along the auroral oval is thought to appear when the electric conductivity of the ionosphere is locally increased under the presence of large scale dawn-to-dusk electric field. The occasional appearance of a localized abnormal geomagnetic disturbance with reversed direction near the geomagnetic pole seems to suggest the occasional reversal of electric field near the outer surface of the magnetospheric tail, especially when the interplanetary magnetic field is northward.     

Particle density in the plasmasphere during quiet periods

Density distribution of plasmaspheric particles in the equatorial plane is derived from a model of plasmaspheric streaming, which may produce S_q current system in the lower ionosphere, and from one integral of motion, which seems to be generally valid for steady-state magnetospheric convection. The results satisfy not only the observed features of S_q variation but also the observed pattern of the density distribution in the magnetospheric equatorial plane during quiet periods.     

Study of total electron content variations over equatorial and low latitude ionosphere during extreme solar minimum

In recent years with the advancement in satellite based navigational applications, study of Total Electron Content (TEC) has gained significant importance. It is well known that due to dynamical behaviour of equatorial and low latitude ionosphere, the levels of ionization is relatively high herein. The sustained decrease in solar extreme ultraviolet radiations during the current minimum is greater than any in recent history. This gives us the opportunity to study the observations of global positioning system total electron content (GPS-TEC) dual frequency signals from the GPS satellites continuously recorded at Trivandrum (an equatorial station) and Delhi (a low latitude station) during the extremely low solar activity period from January 2007 to June 2009. This study illustrates the diurnal, seasonal and annual variations of TEC during the extended solar minimum period. This study also investigates the behaviour of daytime ionosphere around spring and autumn equinoxes at low solar activity period. The results clearly reveal the presence of equinoctial asymmetry which is more pronounced at equatorial station Trivandrum. The diurnal variation of TEC shows a short-lived day minimum which occurs between 0500 to 0600 LT at both the stations. Delhi TEC values show its steep increase and reach at its peak value between 1200 and 1400 LT, while at the equator the peak is broad and occurs around 1600 LT. Further, the daily maximum TEC ranges from about 5 to 40 TEC units at Trivandrum and about 10 to 40 TEC units at Delhi, which correspond to range delay variations of about 1 to 8 m at the GPS L1 frequency of 1.575 GHz. The Maximum values of TEC were observed during spring equinox rather than autumn equinox, showing presence of semi annual variation at both the locations. The minimum values of TEC were observed during the summer solstice at Trivandrum indicating the presence of winter anomaly at equatorial region while Delhi TEC values were minimum during winter solstice showing absence of winter anomaly. Also the TEC values at both the locations have been decreasing since 2007 onwards exhibit good positive correlation with solar activity.     

Asymmetric periodic solutions of the averaged Hill problem with allowance for a planet’s oblateness

We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.     

On the effects of geomagnetic storms and pre storm phenomena on low and middle latitude ionospheric F2

This paper presents some features of the ionospheric response observed in equatorial and mid-latitudes region to two strong geomagnetic storms, occurring during Oct. 19–23, 2001 and May 13–17, 2005 and to understand the phenomena of pre-storm that lead to very intense geomagnetic storms. The result point to the fact that pre-storm phenomena that leads to intense ionospheric storm are; large southward turning of interplanetary magnetic field Bz, high electric field, increase in flow speed stream, increase in proton number density, high pressure ram and high plasma beta. The magnitude of Bz turning into southward direction from northward highly depends upon the severity of the storm and the variation in F2 layer parameter at the time of geomagnetic storm are strongly dependent upon the storm intensity. A detailed analysis of the responses of the ionosphere shows that during the storm periods, foF2 values depleted simultaneously both in the equatorial and mid latitude. Observation also shows that low to moderate variations in ionospheric F2 at the pre-storm period may signal the upcoming of large ionospheric disturbances at the main phase. The ionospheric F2response for low and mid latitude does not show any significant differences during the storm main phase and the pre-storm period. The ionospheric response during the pre-storm period is thought very puzzling. The period is observed to be depleted throughout with low-moderate effect across all the stations in the low and mid latitude.     

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole plus tail magnetic field model, H⁺, He⁺⁺ and O ₁₆ ⁺⁶ ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrace to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory. Results show that the total precipitation rate is sufficient only for particles which enter the magnetosphere near the edges of the current sheet. Small pitch angles are favored at the output plane, but mappings to the auroral ionosphere indicate isotropic pitch angle distributions are favored with some peaking of the fluxes parallel or at other angles to the field lines. Perpendicular auroral pitch angle anisotropies are at times produced by the current sheet acceleration mechanism. Therefore, caution must be used in interpreting all such observations as ‘loss cone-trapping’ distributions. Energy spectra appear to be quite narrow for small cross-tail electric fields, and a little broader as the electric field increases. Comparisons of these results with experimental observations are presented.     

The conditions for the existence of the electric field opposite to the current along the magnetic field lines in the thin plasma

The flow of the current along the magnetic field lines in the thin plasma directed opposite to the electric field is considered. The particles moving to the equatorial plane are supposed to have mirror points above the region of absorption (the ionosphere) and the particles moving to the ionosphere are supposed to have mirror points below the region of absorption. The current, therefore, flows. The functions of the distribution of the electrons and ions are considered to be mono-energetic. The energies of the electrons and the ions and their densities on the boundary of absorption are estimated for the potential difference and for the current density which are typical for the auroral field lines.     

Quiet auroral arcs: Ionosphere effect of magnetospheric convection stratification

A detailed study of the mechanism of electromagnetic stratification of the large-scale stationary magnetospheric convection due to a friction of the convective flow in the ionosphere layer was performed. Magnetosphere-ionosphere interaction was taken into account by means of the effective boundary conditions on the ionosphere top and bottom boundaries including the actual height profile of charge particles velocity in the ionosphere. It has been shown that the magnetospheric convection is stratified into small-scale current sheets which are respective in the linear approximation to an oblique Alfvén wave. The dispersion equation was deduced for the Alfvén mode and its solution obtained determining the space-time scales and the increment of instability. The maximum increment is realized for the disturbances stretched along the convection velocity that is correspondent to the actual orientation of the auroral arcs. In the conditions of rapid growth of Alfvén velocity above the maximum of the ionosphere F layer, it was shown that small-scale disturbances with the transverse scales l_⊥ ? 1 km are localized at the altitudes up to several thousand kilometers whereas the large-scale stratification penetrate into the equatorial plane of the magnetosphere. A mechanism is proposed to intensify the parallel electric field acting at that stratification stage when the field-aligned currents in the Alfvén wave are sufficient to form abnormal resistance along geomagnetic lines of force.     

A new family of periodic oscillations in the Störmer problem: The principal asymmetric

A complete family of asymmetric periodic oscillations of a charged particle in the meridian plane of a magnetic dipole is presented. It begins at a bifurcation with the principal family of symmetric periodic oscillations and terminates in a flat equatorial oscillation. It consists of many stable and unstable segments.     

On the oscillatory motions of the principal plane of the solar corona

We define the principal plane of the solar corona as the equatorial plane of the dipole component of the solar magnetic field at the source surface. The position of this plane defines the orientation of the heliospheric current sheet and the outer solar corona in 3D space, in particular, their inclination with respect to the solar equatorial plane. Their tilt varies from almost zero at solar minimum to almost 90° at solar maximum. But this change is not monotonic; more or less regular oscillations are superimposed onto the average curve. Data on the inclination of the coronal principal plane during 1994–2000 were analyzed. Oscillations with a quasiperiod of 1.3 years were clearly revealed. These oscillations were found to be correlated with variations of the solar rotation rate at the base of the solar convection zone. The latter variations have the same quasi-period of 1.3 years, but they are 1 month out of phase.     

The outer core rotation about an inclined axis from geomagnetic secular variations (Mitteilungen des Zentralinstituts für Physik der Erde,Nr. 1832)

Non-axisymmetric motions of the outer core of the Earth are important for the dynamo problem and the excitation of the decade variations of the polar motion. The components of the vector of a rigid rotation of the outer core about an inclined axis were estimated by a first-order approximation of the frozen- field theory of the geomagnetic secular variation from 1903.5 to 1975.5. The trends and quasi-periodic constituents of these quantities were computed. It was shown that the position and time behaviour of the rotational pole of the outer core differ considerably from the well-know co-ordinates of the dipole axis. Some periods of the equatorial components of the rotational vector are comparable with those of the axial component previously derived for a pure axial rotation. Additionally, the time behaviour of the pole path shows events like the well-known Markowitz wobble but naturally with other extent. These and other results suggested that the investigations are worth to be continued in future by some physical interpretations.     

Modeling African equatorial ionosphere using ordinary Kriging interpolation technique for GNSS applications

The ability to model the ionosphere accurately for single frequency users in satellite applications has gained some appreciable usage, most especially during quiet conditions in a mild (middle latitudes) ionosphere. However, solving the problem of ionosphere for single frequency user of Global Navigation Satellite Systems (GNSS) in equatorial ionization anomaly (EIA) region is of a great concern for space scientists and engineers. Several methodologies have been used to develop models that describe global or regional maps for ionosphere errors in order to mitigate the effect of the errors on GNSS systems. Global or regional ionosphere Maps have been known to be an efficient tool to monitor the delay introduced by the ionosphere in the satellite signals. This research uses the conventional Planar fit and ordinary Kriging methodologies to assess a regional map for ionosphere correction in equatorial African sector. The result obtained is an indication that modified Kriging methodology describes the EIA ionosphere corrections better compared with ordinary Kriging and Planar fit methodologies.     

A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields

Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region (NOAA 10488). We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.     

Energy Release Sites in Magnetic Fields Containing Single Or Multiple Nulls

An ongoing debate is how magnetic energy is released in solar flares, which type of magnetic instabilities are responsible for triggering the energy release, and which magnetic topologies are most likely to host the instabilities. In this connection magnetic reconnection has been a general ingredient, with most of the previous work focussing on 2D reconnection. A natural extension to this is to investigate reconnection in 3D topologies, in particular the behaviour of magnetic nulls and the magnetic topology associated with them. This paper investigates the difference in dynamical behaviour of a numerical domain that either contains a double null-point pair connected by a separator or only a fraction of the separator defined by the null-points. The experiments show that nulls can either accumulate current individually, or act together to produce a singular current collapse along the separator. The implication of these results for the interpretation of coronal data is discussed.     

Diffraction of electromagnetic waves in Schwarzschild's space-time

In order to study the gravitational lens effect in detail this paper investigates the electromagnetic radiation generated by an electric dipole oscillating with high frequency in the Schwarzschild metric outside the horizon. Expressions for the Newman-Penrose tetrad components characterizing the radiation field are derived in a suitable approximation. The Poynting vector is discussed in the region behind the deflecting mass (black hole, neutron star) in the fully coherent case for large distances of source and observer from the centre of the lens. Intensity and gain in the focal region coincide with the corresponding values applying to scalar radiation. An observer sees double images of the source outside the focal region. The results (positions of the images, relative intensities) are compared with those occurring in the case of an incident plane wave (recently treated by Herlt and Stephani) and with the properties of the images in the (geometrical optics) limit of incoherent radiation.