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.     

Observations of forced oscillations of the magnetosphere by a geostationary satellite and an extensive ground magnetometer array

We present results from the analysis of magnetometer measurements of one of the clearest observations of a double resonance Pc4 pulsation to date. The Pc4, with a period of 55 s, was measured by 18 ground magnetometers and also on board the ATS-6 satellite at geostationary orbit. Using a subsequent observation of a second harmonic guided poloidal mode pulsation at ATS-6, we have been able to estimate the plasma density at geostationary orbit. We then calculated periods of theoretical cavity mode resonances in the plasmatrough and the eigenperiods of different wave modes and harmonics at geostationary orbit. We developed a model of the variation of plasma density, and hence eigenperiods, within the magnetosphere which is consistent with these calculations and with the amplitude, phase and ellipticity observations made over the array of ground observatories. In this model we suggest that hydromagnetic field line resonances occur in the plasmatrough and in the plasmasphcre, which are the second and fundamental harmonic guided toroidal mode resonances, respectively. The model also allows us to evaluate the damping experienced by hydromagnetic standing waves in the magnetosphere. The damping is found to be slightly higher than that previously suggested for daytime conditions.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.     

On the diurnal period variation of midlatitude ULF pulsations

Magnetometer studies of the periods of mid-latitude ULF pulsations have produced conflicting results on the variation of the pulsation periods with both latitude and local time. Since the mid-latitude geomagnetic field is not expected to be significantly distorted by the solar wind, the observed diurnal period variations should be determined by changes in the ambient plasma density. We have applied a physically realistic plasmasphere model to the determination of pulsation eigenperiods over a 24-h interval at L=2.3 (appropriate to Wellington, New Zealand). The resulting model pulsation eigenperiods are largest during the day, with minimum and maximum values at 05.00 and 18.00 L.T. respectively. The model predicts a general increase in the eigenperiods during the replenishment of the protonosphere after a period of geomagnetic activity.     

The three-dimensional shape of the magnetopause

Nearly 1000 magnetopause crossings from HEOS-2, HEOS-1, OGO-5 and 5 IMP space-craft covering most of the northern and part of the southern dayside and near-Earth tail magnetopause (X >?15 R_E) have been used to perform a detailed study of the three-dimensional shape and location of the magnetopause. The long-term influence of the solar wind conditions on the average magnetopause geometry has been reduced by normalising the radial distances of the observed magnetopause crossings to an average dynamical solar wind pressure. Best-fit ellipsoids have been obtained to represent the average magnetopause surface in geocentric solar ecliptic (GSE) and (as a function of tilt angle) in solar magnetic (SM) coordinates. Average geocentric distances to the magnetopause for the 1972–1973 solar wind conditions (density 9.4 cm^?3, velocity 450 km s^?1) are 8.8 R_E in the sunward direction, 14.7 R_E in the dusk direction, 13.4 R_E in the dawn direction and 13.7 R_E in the direction normal to the ecliptic plane. The magnetopause surface is tilted by 6.6° ± 2° in a direction consistent with that expected from the aberration effect of the radial solar wind. Our data suggest that the solar wind plasma density and the interplanetary magnetic field (IMF) orientation affect the distance to the polar magnetopause, larger distances corresponding to higher plasma density and southward fields. Our best-fit magnetopause surface shows larger geocentric distances than predicted by the model of Choe et al. [Planet Space Sci. 21, 485 (1973).] normalised to the same solar wind pressure.     

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.     

Solar wind energy transfer regions inside the dayside magnetopause—I. Evidence for magnetosheath plasma penetration

PROGNOZ-7 high temporal resolution measurements of the ion composition and hot plasma distribution in the dayside high latitude boundary layer near noon have revealed that magnetosheath plasma may penetrate the dayside magnetopause and form high density, high β, magnetosheath-like regions inside the magnetopause. We will from these measurements demonstrate that the magnetosheath injection regions most probably play an important role in transferring solar wind energy into the magnetosphere. The transfer regions are characterized by a strong perpendicular flow towards dawn or dusk (depending on local time) but are also observed to expand rapidly along the boundary layer field lines. This increased flow component transverse to the local magnetic field corresponds to a predominantly radial electric field of up to several mV m^?1, which indicates that the injected magnetosheath plasma causes an enhanced polarization of the boundary layer. Polarization of the boundary layer can therefore be considered a result of a local MHD-process where magnetosheath plasma excess momentum is converted into electromagnetic energy (electric field), i.e. we have primarily an MHD-generator there. We state primarily because we also observe acceleration of “cold” ions inside the magnetopause as a result of this radial electric field. A few cases of polarity reversals suggest that the polarization is sometimes quite localized.The perhaps most significant finding is that the boundary layer is observed to be charged up to tens of kilovolts, a potential which may be highly variable depending on e.g. the presence of a momentum exchange by the energy transfer regions.     

Transmission of Alfvén waves through the rotational discontinuity at magnetopause

The reflection and refraction of MHD waves through an “open” magnetopause (rotational discontinuity) is studied. It is found that most of the incident wave energy can be transmitted through the open magnetopause. A transverse Alfvén wave (or a compressional magnetosonic wave) from the solar wind incident upon the open magnetopause would generally lead to the generation of both the transverse Alfvén and compressional magnetosonic waves in the magnetosphere. Transmission of Alfvén waves in the coplanar rotational discontinuity is studied in detail. The integral power of the Alfvén-wave transfer is found to be proportional to the open magnetic flux of the magnetosphere and is typically ～ 1% of the power of the total electromagnetic energy transfer through the open magnetopause. The transmitted wave power may contribute significantly to the geomagnetic pulsations observed on the ground, especially in the open-field-line region.     

Evidence of electrical activity on Titan drawn from the Schumann resonances sent by Huygens probe

A procedure is shown for extracting weak resonances from the responses of electromagnetic systems excited by electric discharges. The procedure, based on analysis of the late-time system response, is first checked using an analytical function and later with the data for the electric field generated by the computational simulation of Titan's atmosphere using the Transmission Line Matrix (TLM) method. Finally, the low frequency spectrum of the natural electric field in Titan's atmosphere sent by the mutual impedance sensor (MIP) included in the Huygens probe is analyzed employing this technique. The MIP sensor was initially designed to measure the horizontal component of the electric field during a quiet descent. Fortunately, the swinging that occurred during the descent allowed the MIP to measure the radial component of the electric field mixed with the horizontal one. Application of the late-time analysis technique shown in this paper confirms the signature of lightning reported by preliminary data observations, bringing out the expected eigenfrequencies of the Titan-ionosphere electromagnetic cavity, known as Schumann resonances. These resonances are the resonant frequencies of the lower TM^r (transverse magnetic to r) modes, which are quasi-transverse electromagnetic modes because they present vertical or radial components of the electric field two orders of magnitude higher than the associated horizontal, azimuthal and zenithal, components. The sequence of Schumann resonances is unique for each celestial body with an ionosphere, since these resonances are fully determined by the dimensions of the planet or satellite and the corresponding atmospheric conductivity profile. Detecting these frequencies in an atmosphere is clear proof of electrical activity, since it implies the existence of an electromagnetic-energy source, which is essential to create and maintain them.     

The structure of the magnetopause

The solar wind is a magnetized flowing plasma that intersects the Earth's magnetosphere at a velocity much greater than that of the compressional fast mode wave that is required to deflect that flow. A bow shock forms that alters the properties of the plasma and slows the flow, enabling continued evolution of the properties of the flow on route to its intersection with the magnetopause. Thus the plasma conditions at the magnetopause can be quite unlike those in the solar wind. The boundary between this “magnetosheath” plasma and the magnetospheric plasma is many gyroradii thick and is surrounded by several boundary layers. A very important process occurring at the magnetopause is reconnection whereby there is a topological change in magnetic flux lines so that field lines can connect the solar wind plasma to the terrestrial plasma, enabling the two to mix. This connection has important consequences for momentum transfer from the solar wind to the magnetosphere. The initiation of reconnection appears to be at locations where the magnetic fields on either side of the magnetopause are antiparallel. This condition is equivalent to there being no guide field in the reconnection region, so at the reconnection point there is truly a magnetic neutral or null point. Lastly reconnection can be spatially and temporally varying, causing the region of the magnetopause to be quite dynamic.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

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.     

Giant PC5 pulsations in the outer magnetosphere: A survey of HEOS-1 data

Magnetic field measurements from 133 low-latitude transits of the HEOS-1 satellite through the magnetosphere have been used to analyse the low-frequency pulsation activity in the outer regions of the geomagnetic field. Providing full longitude coverage in the sunward hemisphere at geocentric distances larger than ~7.5 R_e, this survey complements previous low-frequency pulsation data from satellites at smaller geocentric distances. Several giant PC5 events, each being mainly compressional and lasting 1–2 hr, are described in detail and it is shown that this phenomenon is relatively common in the 8–12 R_e, geocentric distance range near dusk. A depression of the ambient field magnitude always accompanied the events, suggesting that they are associated with a region of enhanced plasma pressure. The properties of these wave events are compared with the predictions of current micropulsation theories involving a Kelvin-Helmholtz generation mechanism and field-line resonance. Unlike the PC5 events observed nearer Earth, these events were not obviously related to periods of enhanced geomagnetic activity.     

The stability of the pristine magnetopause

A MHD theory of combined Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities for a transition layer with two different scale lengths (Δ and δ for the variation of velocity/magnetic fields and density, respectively) is presented. The study is motivated by reports of magnetopauses with no low latitude boundary layer, in which a sharp density drop over a distance δ?Δ is observed (“pristine” magnetopauses (J. Geophys. Res. 101 (1996) 49). The theory ignores compressibility effects and applies to subsonic regions of the dayside magnetopause. The RT effect is included to account for temporary periods of acceleration of the magnetopause, caused by sudden changes of the solar wind dynamic pressure. For small wavelengths λ, such that δ?λ?Δ, a WKB solution shows that the velocity gradient operates, together with magnetic tensions, to attenuate or even stabilize the Rayleigh-Taylor instability within a certain wavelength range. An exact dispersion relation for flute modes, valid for all λ, in the form of a fourth order polynomial for the complex frequency ω, is obtained from a model with a constant velocity gradient, dV/dy within Δ, and with δ→0. Flute modes are possible because of the existence of bands of very small magnetic shear on the dayside magnetopause (J. Geophys. Res. 103 (1998) 6703). The exact solution allows for a study of the change of the action of the velocity gradient with λ from the long-λ range where dV/dy is KH destabilizing to the short-λ range where dV/dy produces a stabilizing effect. Both, the WKB approximation and the well known tangential discontinuity model (Δ→0) are recovered as limiting cases of the exact solution. Properties of the KH and RT instabilities, for different density ratios on either side of the magnetopause, are described. For flute modes, at very small λ the RT instability grows faster and becomes the dominant effect. However, it is shown that the growth rate remains bounded at a finite value as λ→0, when a theory with a finite δ model is considered. To study configurations with finite, arbitrary, δ/Δ ratios, the MHD perturbation equations are solved numerically, using hyperbolic tangent functions for both the density and velocity transitions across the magnetopause. To examine the influence of different δ/Δ ratios on the growth rates of KH and RT, calculations are performed for different δ/Δ, with and without acceleration, and for two different density ratios. It is found that the general features exhibited by the constant dV/dy model, are confirmed by these numerical solutions. The stability of pristine magnetopauses, and the possibility of observing some theoretical predictions during magnetopause crossings in ongoing missions, are discussed.     

Modeling Magnetic Tower Jets in the Laboratory

The twisting of magnetic fields threading an accretion system can lead to the generation on axis of toroidal field loops. As the magnetic pressure increases, the toroidal field inflates, producing a flow. Collimation is due to a background corona, which radially confines this axially growing “magnetic tower”. We investigate the possibility of studying in the laboratory the dynamics, confinement and stability of magnetic tower jets. We present two-dimensional resistive magnetohydrodynamic simulations of radial arrays, which consist of two concentric electrodes connected radially by thin metallic wires. In the laboratory, a radial wire array is driven by a 1 MA current which produces a hot, low density background plasma. During the current discharge a low plasma beta (β < 1), magnetic cavity develops in the background plasma (β is the ratio of thermal to magnetic pressure). This laboratory magnetic tower is driven by the magnetic pressure of the toroidal field and it is surrounded by a shock envelope. On axis, a high density column is produced by the pinch effect. The background plasma has >rsim1, and in the radial direction the magnetic tower is confined mostly by the thermal pressure. In contrast, in the axial direction the pressure rapidly decays and an elongated, well collimated magnetic-jet develops. This is later disrupted by the development of m = 0 instabilities arising in the axial column.     

ULF pulsation mode coupling in the ionosphere and magnetosphere

The effect of realistic ionospheric Hall conductances on axisymmetric toroidal mode hydromagnetic wave resonances is investigated. The toroidal modes couple to evanescent poloidal modes near the ionospheres such that the composite modes resonate at the constant frequencies of the corresponding single-field-shell resonances for zero Hall conductance. A model for these composite modes is developed which has narrow but finite latitudinal resonance widths such as to make the modes valid solutions of the hydromagnetic equations. The modes also suggest that “shell” solutions can realistically describe such properties of real pulsations as frequency, damping, phase variation along the field-line and node-antinode behaviour at the ionospheres. Estimates of ionospheric coupling strength are obtained and compared with magnetospheric coupling strength. It is found that magnetospheric coupling dominates ionospheric coupling for any single non-axisymmetric mode. However, ionospherically coupled axisymmetric modes should be necessary components of the Fourier sum of modes required to model any real pulsation of low to moderate apparent azimuthal wave number.Estimates of the range of magnetospheric coupling strength are obtained for pulsations under a variety of conditions.     

Dependence of the magnetopause position on the southward interplanetary magnetic field

The distance to the dayside magnetopause is statistically analyzed in order to detect the possible dependence of the dayside magnetic flux on the polarity of the interplanetary magnetic field. The effect of changing solar wind pressure is eliminated by normalizing the observed magnetopause distances by the simultaneous solar wind pressure data. It is confirmed that the normalized size of the dayside magnetosphere at the time of southward interplanetary magnetic field is smaller than that at the time of northward interplanetary magnetic field. The difference in the magnetopause position between the two interplanetary field polarity conditions ranges from 0 to 2R_E. Statistics of the relation between the magnetopause distance and the magnetic field intensity just inside the magnetopause testifies that the difference in the magnetopause position is not due to a difference in the magnetosheath plasma pressure. The effect of the southward interplanetary magnetic field is seen for all longitudes and latitudes investigated (|λ_GM|? 45°, |φ_SM|? 90°). These results strongly suggest that a part of the dayside magnetic flux is removed from the dayside at the time of southward interplanetary magnetic field.     

Long-period magnetic pulsations generated in the magnetospheric boundary layers

Long-period hydromagnetic waves can be excited by the velocity shear instability in the magnetospheric boundary layers, where the penetrated bulk flow of the solar wind comprises a fairly strong velocity shear. Model spaces of the boundary layers are considered to estimate amplification rates on the HM waves in the low-latitude flank-side and in the dayside high-latitude and mantle-side boundary layers, where the ambient magnetic field is assumed to be perpendicular and parallel to the bulk flow of the solar wind, respectively. Wave characteristics of the HM waves are also investigated for the k-vector almost normal to the magnetopause.The localized HM waves in the Pc 3–4, Pc 4–5 and Pc 6 frequency ranges, of which group velocities are mostly parallel to the plane in the ambient magnetic field and the bulk flow directions, i.e., parallel to the magnetopause, are sufficiently amplified in the dayside low- and high-latitude, in the low-latitude flank-side, and in the mantle-side boundary layers, respectively. A left-handed toroidal (transverse) and a right-handed poloidal (compressional) mode of long-period $\text{(T ? 120}\text{s}\text{)Ω}{}_{\mathrm{A}}$-wave are generated in the dawn- and the duskflank boundary layers, respectively, where the k-vector of Alfvénic signals was assumed to be almost in the Archemedean spiral direction. The localized compressional HM waves in the Pc 3–4 range indicate both lefthanded and right-handed polarizations in the dayside boundary layer, which are functions of the k-vector of the waves and the sense of the velocity shear. The variance directions of perturbation fields of the HM waves in the magnetospheric boundary layers tend to be nearly parallel to the magnetopause. These localized HM waves can propagate into the high-latitude ionosphere. We conclude that the localized HM waves driven by the velocity shear instability in the magnetospheric boundary layers are the most probable source of the daytime Pc 3–5 magnetic pulsations in the outer magnetosphere.     

A Comparative Analysis of Ground, Magnetospheric and Interplanetary Observations of Long Period Magnetic Oscillations

Continuous measurements of the geomagnetic field variations at ground stations are important to investigate several aspects of magnetospheric dynamics related to variations in the solar wind conditions which, ultimately, originate from the Sun. We present a comparative analysis of geomagnetic field measurements at several ground stations with simultaneous magnetospheric and interplanetary observations in order to understand the origin and characteristics of the observed fluctuations. The results suggest that long period geomagnetic field fluctuations can be directly driven by solar wind density fluctuations at the same frequencies via the modulation of the magnetopause current. We also discuss the possible occurrence of additional contributions related with cavity/waveguide resonances of the entire magnetosphere as well as those of resonance processes of the geomagnetic field lines.