A dipole field model for axisymmetric alfvén waves with finite ionosphere conductivities

An axisymmetric model for approximate solution of the magnetospheric Alfvén wave problem at latitudes above the plasmapause is proposed, in which a realistic dipole geometry is combined with finite anisotropic ionosphere conductivities, thus bringing together various ideas of previous authors. It is confirmed that the axisymmetric toroidal and poloidal modes interact via the ionospheric Hall effect, and an approximate method of solution is suggested using previously derived closed solutions of the uncoupled wave equations.A solution for zero Hall conductivity is obtained, which consists of sets of independent shell oscillations, regardless of the magnitude of the Pedersen conductivity. One set reduces to the classical solutions for infinite Pedersen conductivity, while another predicts a new set of harmonics of a quarter-wave fundamental, with longer eigenperiods than the classical solutions for a given L-shell.     

Accurate approximate formulae for toroidal standing hydromagnetic oscillations in a dipolar geomagnetic field

Calculations of the toroidal eigenmodes of oscillation of the magnetospheric plasma have been important in explaining the nature of Pc3, Pc4 and Pc5 geomagnetic pulsations. In this paper perturbation solutions of the governing equations are presented. These are much more accurate than the WKB approximation which has often been used, and much simpler to compute than the numerical solutions which have been used. A method of including the finite ionospheric conductivity is also presented.     

Local time asymmetry in the characteristics of Pc5 magnetic pulsations

The wave characteristics of Pc5 magnetic pulsations are analyzed with data of OGO-5, ISEE-1 and -2 satellites. The toroidal modes (δB_D >δB_H) of Pc5 pulsations are observed at a higher magnetic latitude in the dawnside outer magnetosphere. The compressional and poloidal modes (δB_z.dfnc; ～ δB_H >δB_D) of Pc5 pulsations are mostly observed near the magnetic equator in the duskside outer magnetosphere. This L.T. asymmetry in the occurrence of dominant modes of Pc5's in space can be explained by the velocity shear instability (Yumoto and Saito, 1980) in the magnetospheric boundary layer, where Alfvénic signals in the IMF medium are assumed to penetrate into the magnetospheric boundary layer along the Archimedean spiral. The asymmetrical behaviour of Pc5 pulsation activity on the ground across the noon meridian can be also explained by the ionospheric screening effect on the compressional Pc5 magnetic pulsations. The compressional modes with a large horizontal wave number in the duskside magnetosphere are expected to be suppressed on the ground throughout the ionosphere and atmosphere.     

The effect of non-uniform ionospheric conductivity on standing magnetospheric Alfven waves

We look at time-dependent normal mode solutions to the Alfven wave equation in a uniform magnetic field, between planar ionospheres. In particular, the effect of sharp gradients in ionospheric conductivity on the spatial and temporal structure of the waves is considered. We show that the electric field of the wave must always be perpendicular to any conductivity discontinuities present, and that this is achieved by the generation of circularly polarized Alfven waves at the discontinuity. The results are applied to an ionospheric strip of high conductivity; this being relevant to Pi2s.     

A high resolution study of continuous pulsations in the European sector

Complex demodulation has been described in detail and applied to Pi2 pulsations in a previous paper by Beamish et al. (1979). The technique is now extended to demonstrate spatiotemporal variations in the fundamental characteristics of Pc3 and Pc4 pulsations along a meridional profile extending from the U.K. to Iceland. With the exception of a high latitude Pc4 coupled resonance the results are consistent with a ?90° Hughes rotation (introduced by the ionosphere) of magnetospheric toroidal line resonances. Furthermore, the ionosphere appears capable of smoothing away the polarisation reversal which would be expected across such amplitude maxima within the plasmasphere. However, a toroidal line resonance in the Pc3 period range about which a sense of polarisation reversal is clearly observed on the ground is suggested as occurring at the plasmapause. This is accounted for in terms of the width of the resonance structure.     

Transient ULF pulsation decay rates observed by ground based magnetometers: The contribution of spatial integration

Theoretical studies suggest that Joule dissipation in the ionosphere is the major source of damping for resonant ULF pulsations. The decay rates of transient pulsations (i.e. short-lived pulsations with latitude dependent periods) observed by ground based magnetometers are however generally larger than those predicted, and also larger than those observed in the magnetosphere. We have modelled the integration effects of ground based magnetometers on transient pulsations by considering empirical models of the associated ionospheric currents. The simulated ground magnetometer data show a smearing of the amplitude and period variations, which is more pronounced for smaller scale (specifically latitudinal) variations. The period increase with latitude is reduced, and may even be eliminated over appreciable latitude ranges. For all spatial scales the observed decay rates are typically 2–3 times larger than the true values, due to the additional decay resulting from spatial integration of the incoherent transient pulsations. Estimates of the ionospheric Pedersen conductance based on ground magnetometer observations of decay rates are correspondingly too small, and spurious gradients may be introduced. The present calculations reconcile observed decay rates on the ground with those predicted using the assumption that Joule dissipation is the dominant damping mechanism for toroidal mode resonant oscillations.     

The effect of asymmetry on toroidal hydromagnetic waves in a dipole field

The meridional and azimuthal electric wave fields are considered as the characteristic toroidal and poloidal components. Neglecting the exchange of energy between these fields leads to a toroidal mode wave equation which retains the principal longitudinal or asymmetric contribution. The asymmetric spectrum appears as a logical extension of the results for the symmetric field line oscillations. The model for this study consists of a dipole field magnetized plasma, whose density is commensurate with conditions in the plasmapause. Eigenperiods are calculated for a broad range of asymmetric modes. Because of the similarity in the latitudinal variation between the symmetric and asymmetric periods, it is imperative to revise current idealized magnetospheric models and incorporate such similarity in future models.     

Impulse-excited hydromagnetic cavity and field-line resonances in the magnetosphere

We present detailed numerical results from a model which determines the time development of hydromagnetic waves within a hemi-cylindrical magnetospheric cavity subject to a short-duration compressional stimulus at the magnetopause. The model allows a realistic radial variation of Alfvén speed, arbitrary axial asymmetry, and the inclusion of ionospheric Joule dissipation.The results show the development of a set of compressional cavity resonances, and their coupling to a corresponding set of field-line resonances at positions where the cavity eigenperiods match the uncoupled field-line eigenperiods. Transient solutions having variable period with radial distance are important in establishing the field-line resonances, and can be locally dominant in certain regions of the outer magnetosphere.The variation with axial wavenumber m of the cavity eigenperiods is obtained, and it is shown that the magnetopause impulse drives the field-line resonances most efficiently for m ∼ 3. This suggests that small azimuthal wavenumbers are important in the terrestrial magnetosphere under analogous conditions. A variety of waveform and polarisation diagrams is given to aid in observational identification of such coupled resonances.     

Ballooning modes in the inner magnetosphere of the Earth

In this paper the low-frequency ideal MHD (magnetohydrodynamical) perturbations in the inner magnetosphere of the Earth are studied. The set of partial differential equations obtained from the MHD equations in the ballooning approximation and the dipole model of the geomagnetic field is used for this purpose. These equations describe both small-scale and large-scale perturbations in the magnetospheric plasmas. In the “cold” plasma approximation the obtained equations describe poloidal and toroidal standing Alfvén modes. The account of plasma pressure leads to the appearance of an additional type of oscillations—the slow magnetosonic modes. The stability of the magnetospheric plasma with respect to the ballooning perturbations was analyzed. We describe the ballooning perturbations taking into account a coupling between the poloidal Alfvén modes and the slow magnetosonic modes.     

The role of the Hermanus Magnetic Observatory in geomagnetic field research

Geomagnetic field research carried out at the Hermanus Magnetic Observatory over the past decade is reviewed. An important aspect of this research has been the study of geomagnetic field variations, with particular emphasis on ULF geomagnetic pulsations. Features of geomagnetic pulsations which are unique to low latitude locations have been investigated, such as the cavity mode nature of low latitude Pi 2 pulsations and the role played by ionosphericO ⁺ ions in the field line resonances responsible for Pc 3 pulsations. A theoretical model has been developed which is able to account for the observed relationships between geomagnetic pulsations and oscillations in the frequency of HF radio waves traversing ionospheric paths. Other facets of the research have been geomagnetic field modelling, aimed at improving the accuracy and resolution of regional geomagnetic field models, and the development of improved geomagnetic activity indices.     

Latitude variation of the spectral components of auroral zone Pi2

Evidence is presented from spectral analysis of Pi2 pulsations detected during a substorm by the University of Alberta meridian chain of magnetometers to support the conclusion that at auroral latitudes there is no apparent correlation between the principal spectral components of Pi2 pulsations and the latitude of the observations. From these data we infer that the Pi2 magnetic variations observed at the Earth's surface are not generated by simple MHD eigenoscillations of magnetospheric field. As well, the data show clear contributions to the Pi2 pulsation spectrum by ionospheric currents. These observations lead to the suggestion that Pi2 pulsation spectra are produced by the sudden changes in magnetospheric and ionospheric current systems which take place at the beginning of a substorm.     

Pi 2 pulsations: High latitude results

A review of recent experimental results from studies of high latitude Pi 2 pulsations indicates that these pulsations are fundamentally related to the initiation of the auroral breakup and substorm. At high latitudes, the Pi 2's show their peak intensities in the region where the breakup begins and appear to remain in this region after the breakup has spread poleward. In addition, the Pi 2's occur simultaneously with, or before all other ionospheric phenomena associated with the breakup. The field aligned and ionospheric currents associated with the Pi 2 resemble those of a typical substorm, but the ionospheric currents are phase shifted compared to the field aligned current. The periodic oscillations of the Pi 2's are probably caused by a reflection of the initial field aligned current pulse from the auroral ionosphere. This pulse is trapped on dipolar field lines leading to multiple reflections from North and South auroral ionospheres.     

Hydromagnetic wave coupling in the magnetosphere—Plasmapause effects on impulse-excited resonances

Recent analytical and numerical modelling has demonstrated the possibility that impulsively-stimulated compressional hydromagnetic cavity resonances can drive local field-line resonances in the magnetosphere. This paper extends the modelling to include axisymmetric plasmapause structures with realistic radial variation in the magnetospheric cavity. The results show that: (a) the plasmapause plays an important rôle in determining which cavity resonances are dominant; (b) when the wave fields are significantly non-axisymmetric, additional cavity resonances are evident which are at least partly trapped within the plasmasphere; (c) the position of the plasmapause determines where (and whether) cavity resonances couple significantly to field-line resonances; (d) for the small “azimuthal” wavenumber chosen, there is no evidence of a compressional surface wave on the plasmapause.     

Spatial and temporal structure of a high-latitude transient ULF pulsation

Auroral radar observations of transient ULF pulsations with latitudinally varying period have recently been reported. An event of this type is analysed using data from the Scandinavian Magnetometer Array, the STARE radar, and the GEOS-2 satellite. The magnetometers show long-period (～450 s) oscillations consistent with the pulsations observed in the ionosphere using STARE, and confirm that the geomagnetic field shells are resonating in the toroidal mode. There is also a localised, small-amplitude component with 250-s period South of the STARE pulsations. Electric field measurements at GEOS-2 show only an impulsively stimulated pulsation of 250-s period. The wave fields at GEOS-2 imply that the satellite was earthward of a localised toroidal standing-wave resonance, which mapped to the ionosphere at least one degree South of the expected position. A radial profile of equatorial plasma mass density is inferred from the GEOS-2 and STARE results. This shows a radially increasing density near GEOS-2, and a radially decreasing density outside the satellite position.An interpretation of the event is given in which a tailward propagating hydromagnetic impulse directly stimulates field shells outside 7 R_E to oscillate at their eigenperiods. In the region of increasing density near GEOS-2, a relatively highly-damped surface wave is excited. This feeds energy rapidly into a narrow monochromatic toroidal field-line resonance, which subsequently decays more slowly through ionospheric dissipation.     

Comments on the proton whistler generation process

The problem of the propagation of an electromagnetic wave originating for instance in a lightning flash through the ionospheric medium is analysed in order to understand the formation at high ionospheric altitudes of the so-called proton whistler. It is shown that the accessibility of the hydrodynamic (or kinetic) proton resonance at the satellite altitude requires that a mode conversion process must take place slightly above the transition region separating the one ion (O⁺) from the two ion (O⁺ + H⁺) component plasmas. Moreover, the transformation conditions in the wave conversion region imply that the magnetic field should be (almost) perpendicular to the density gradient. Otherwise, the incident electromagnetic wave will never reach the satellite altitude in the frequency range of the proton whistler. However, some former proton whistler theories have postulated that the signal is the result of simple ionospheric propagation effects, in contradiction with the above results. These former proton whistler theories are reviewed and it is shown that the basic flaw in these theories lies in that the incident electromagnetic wave has been supposed from the beginning to have reached the high ionospheric altitudes where is located the satellite without being influenced by the lower ionospheric layers. Some various aspects, like the high variability of the wave electric to magnetic field ratio and the harmonics bands as observed by Injun are analysed in the light of the obtained results. Finally, numerical solutions of the wave dispersion relation for both the fast hydrodynamic mode (the extraordinary mode) and the slow ion kinetic mode are presented which shows that a coupling process between the two modes may take place at various frequencies between the O⁺ and the H⁺ gyrofrequencies.     

Phase variation of ULF pulsations along the geomagnetic field-line

Some points are discussed concerning possible sources of confusion in earlier theory on ULF pulsations with finite ionosphere conductances. Behaviour of the time-integrated Poynting vector in this theory is examined in detail. It is shown that, whenever ionosphere conductances are asymmetric, the time-integrated Poynting vector is zero at a point (termed the “null-point”) displaced away from the equatorial plane. The wave phase behaviour along the field-line is consistent with a picture of travelling-wave components originating at the null-point and carrying energy to the ionospheres.Higher harmonics of resonances with asymmetric conductances are discussed from the point of view of comparing electric field phase using measurements from geostationary satellites and STARE-type auroral radars. The null-point behaviour suggests that some surprising phase differences may be obtained in certain cases between equatorial plane and ionosphere.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

Day-side ionospheric conductivities at Mars

We present estimates of the day-side ionospheric conductivities at Mars based on magnetic field measurements by Mars Global Surveyor (MGS) at altitudes down to ∼100 km during aerobraking orbits early in the mission. At Mars, the so-called ionospheric dynamo region, where plasma/neutral collisions permit electric currents perpendicular to the magnetic field, lies between 100 and 250 km altitude. We find that the ionosphere is highly conductive in this region, as expected, with peak Pedersen and Hall conductivities of 0.1-1.5 S/m depending on the solar illumination and induced magnetospheric conditions. Furthermore, we find a consistent double peak pattern in the altitude profile of the day-side Pedersen conductivity, similar to that on Titan found by Rosenqvist et al. (2009). A high altitude peak, located between 180 and 200 km, is equivalent to the terrestrial peak in the lower F-layer. A second and typically much stronger layer of Pedersen conductivity is observed between 120 and 130 km, which is below the Hall conductivity peak at about 130-140 km. In this altitude region, MGS finds a sharp decrease in induced magnetic field strength at the inner magnetospheric boundary, while the day-side electron density is known to remain high as far down as 100 km. We find that such Titan-like behaviour of the Pedersen conductivity is only observed under regions of strongly draped magnetospheric field-lines, and negligible crustal magnetic anomalies below the spacecraft. Above regions of strong crustal magnetic anomalies, the Pedersen conductivity profile becomes more Earth-like with one strong Pedersen peak above the Hall conductivity peak. Here, both conductivities are 1-2 orders of magnitude smaller than the above only weakly magnetised crustal regions, depending on the strength of the crustal anomaly field at ionospheric altitudes. This nature of the Pedersen conductivity together with the structured distribution of crustal anomalies all over the planet should give rise to strong conductivity gradients around such anomalies. Day-side ionospheric conductivities on Mars (in regions away from the crustal magnetic anomalies) and Titan seem to behave in a very similar manner when horizontally draped magnetic field-lines partially magnetise a sunlit ionosphere. Therefore, it appears that a similar double peak structure of strong Pedersen conductivity could be a more general feature of non-magnetised bodies with ionised upper atmospheres, and thus should be expected to occur also at other non-magnetised terrestrial planets like Venus or other planetary bodies within the host planet magnetospheres.     

On the resonant modes of a cavity and the dynamical properties of micropulsations

Certain classes of micropulsations are customarily explained in terms of guided (toroidal) and isotropic (poloidal) hydromagnetic waves m the magnetosphere. The physical properties of these waves are not well understood and their utility in explaining observed polarization patterns is questionable. In an effort to understand and explain the physics underlying these modes, a study is made of a cylindrical cavity (the hydromagnetic wedge), filled with a plasma having a large but finite conductivity and magnetized by an azimuthal magnetic field. Coupling between the toroidal and poloidal modes is effected by the inclusion of the Hall current in the generalized Ohm's law. Physically meaningful solutions to the wave equation are obtained and the toroidal eigenfunctions are demonstrated to be non-degenerate and well-behaved throughout the configuration, and exhibit for each mode a unique spatial resonance whose location, given by a line of force, is specified by the corresponding eigenvalue. The non-degenerate, discrete and spatially independent eigenvalues for the modes are shown to obey a selection rule that limits the spectrum. For a given mode, the states of polarization of the transverse field are determined and it is shown (as has been observed) that, depending on the line of force singled out, the magnetic polarization may be linear, elliptical or circular, right or left-handed, and whatever the state, it is immutable along the line of force. More complicated polarization patterns are derived and explained by superposing different modes vectorially. Classical concepts such as guided and isotropic modes and vibrating field lines are reinterpreted and evaluated in terms of the model. To examine the dependence of modal amplitude on source, the amplitude is expressed in terms of a sinusoidal driving pressure for a simple steady-state case. Symmetries of the model and the magnetosphere are specified and the detailed numerical results are ‘scaled’ for plasmaspheric application. The resonant spectrum, encompassing pc 2–4, is described and the variation of period spectrum with magnetic latitude and activity is presented. The agreement between the semi-quantitative analysis and the observational results is sufficiently close to indicate that the basic physics of the model encompasses the fundamental dynamics of pc activity.     

On the asymmetric nature of micropulsations—I. the spectrum

This paper is based on the postulate that the natural electromagnetic radiation observed in the micropulsation band is accounted for by the eigenmodes of a resonant cavity in the Earth's outer atmosphere, just as the adjacent ELF part of the spectrum is explained by resonances in the Earth-ionosphere cavity. The inner edge of the plasma sheet (the Alfvén layer) forms an effective resonant cavity which we call the Alfvénsphere. Its complex medium is characterized by two parameters, effective conductivity, and effective Alfvén speed: its quasi-stationary states are specified by two state parameters, effective cavity size, and effective time scale for magnetospheric processes, and in principle, they can be evaluated from the power spectra of observed micropulsations. Because of the complex geometry of the cavity and the fact that the vector hydromagnetic wave equation for an asymmetric electric field is not simply separable in spherical and orthogonal dipole coordinates (and the spatial boundary value problem is virtually insoluble), a model is developed which contains the essential physics and admits of tractable equations. A coupling scheme is defined and discussed which permits one to study the eigenvalue equation under conditions of weak and strong coupling as well as the uncoupled case. Emphasis is placed on the most difficult weakly-coupled case because the results can be readily compared with the uncoupled case. The complex dispersion relation-ship is presented and complex eigenvalues are calculated. It is shown that for any mode (v, i, m), the fundamental (i = 1) appears at the highest latitude and the highest harmonic (i = i_max) appears at the lowest latitude. Further it is shown that the fundamental and harmonics are split into multiplet frequency states, clustered at different latitudes, and ordered at a particular latitude by the asymmetric label m. This property is used to explain beating and atitudinal and longitudinal variations in pearl pulsations. It is demonstrated that the east-west magnetic component of the perturbed magnetic field (for any mode) has two spatial resonances (logarithmic and asymmetric) and this feature can be used to derive and interpret the T cos²Θ = const law. This in turn suggests a method for ordering the east-west component power spectra for a station at any latitude below 70° N mag. in terms of v, and evaluating the corresponding phenomenological state parameters. The inescapable conclusion appears to be that there is no intrinsic difference between the ‘different’ classes of pulsations; they are simply the excited eigenmodes of the Alfvénsphere for different quasi-stationary states.