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.     

Magnetization of celestial bodies with special application to the primeval Earth and Moon

The magnetic fields of celestial bodies are usually supposed to be due to a ‘hydromagnetic dynamo’. This term refers to a number of rather speculative processes which are supposed to take place in the liquid core of a celestial body. In this paper we shall follow another approach which is more closely connected with hydromagnetic processes well-known from the laboratory, and hence basically less speculative. The paper should be regarded as part of a general program to connect cosmical phenomena with phenomena studied in the laboratory. As has been demonstrated by laboratory experiments, a poloidal magnetic field may be increased by the transfer of energy from a toroidal magnetic field through kink instability of the current system. This mechanism can be applied to the fluid core of a celestial body. Any differential rotation will produce a toroidal field from an existing poloidal field, and the kink instability will feed toroidal energy back to the poloidal field, and hence amplify it. In the Earth-Moon system the tidal braking of the Earth's mantle acts to produce a differential angular velocity between core and mantle. The braking will be transferred to the core by hydromagnetic forces which at the same time give rise to a strong magnetic field. The strength of the field will be determined by the rate of tidal braking. It is suggested that the magnetization of lunar rocks from the period ?4 to ?3 Gyears derives from the Earth's magnetic field. As the interior of the Moon immediately after accretion probably was too cool to be melted, the Moon could not produce a magnetic field by hydromagnetic effects in its core. The observed lunar magnetization could be produced by such an amplified Earth field even if the Moon never came closer than 10 or 20 Earth's radii. This hypothesis might be checked by magnetic measurements on the Earth during the same period.     

Quantitative magnetospheric magnetic field modelling with toroidal and poloidal vector fields

Toroidal and poloidal vector fields allow divergence free magnetic field representations in regions where currents flow. We derive general magnetospheric magnetic fields using combinations of spherical harmonic expansions of the toroidal and poloidal fields. Adding restrictive conditions like the field line topology symmetry or the magnetic field measurements, more specific magnetospheric magnetic field models can be derived. Two examples of this technique are given : an axisymmetric model with a ring current in the equatorial region and a time-dependent model of the Earth's magnetosphere. Our results are compared with the Olson-Pfitzer model.     

Observational features of field line resonances excited by solar wind pressure variations on 4 September 1984

In the course of the magnetic storm of 4 September 1984, after an inverse sudden impulse (SI), geomagnetic pulsations in the Pc5-frequency range were observed at magnetometer stations in the local evening sector. They occurred at L-values of 6, and lasted for several hours, their period increasing from about 320 to 550 s. In this study, two events of enhanced activity are discussed in some detail. During the 16:00 U.T. event, a favourable position of the AMPTE/IRM spacecraft allows conjugate observations in the Northern and Southern Hemispheres and in the magnetosphere. This constellation permits a precise determination of the wave mode. During a later intensification around 18:00 U.T., the AMPTE/CCE spacecraft near local noon monitored poloidal waves, obviously driving the pulsations on the ground. Generally, the observations are consistent with the theory of field line resonance. They are interpreted as being excited by pressure variations in the solar wind. The hydromagnetic cavity mode is assumed to link the magnetopause surface motions to the field line resonances.     

On axisymmetric hydromagnetic equilibria

The physical characteristics of possible axisymmetric equilibria are examined on the basis of the integrals of hydromagnetic equations. It is shown for nearly spherical configurations that a surface differential rotation is possible only in the absence of a meridional circulation with either purely toroidal or purely poloidal magnetic field. In the presence of a meridional circulation, it is shown that no surface rotation or constant rotation is possible if the magnetic field is purely toroidal, and that no rotation is possible if the magnetic field is purely poloidal. A brief discussion is given on the possible solutions including the case of stellar winds with force-free magnetic fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.     

Torsional Alfvén modes in dipole and toroidal magnetospheres

Propagation of torsional Alfvén waves in the magnetosphere is examined for two models of the Earth's magnetic field, one where the field is toroidal, the other being a dipole field. Both models yield magnetically guided torsional wave modes which are strongly localized in all directions transverse to the steady magnetic field. The transverse structure is determined by a self-consistent solution of the ideal MHD equations. It is shown that the torsional wave is guided even when b is finite, where b is the component of the wave magnetic field in a direction parallel to the steady magnetic field.     

Wave propagation in the magnetosphere of Jupiter

The magnetosphere of Jupiter has been the subject of extensive research in recent years due to its detectable radio emissions. Observations in the decimetric radio band have been particular helpful in ascertaining the general shape of the Jovian magnetic field, which is currently believed to be a dipole with minor perturbations. Although there is no direct evidence for thermal plasma in the magnetosphere of Jupiter, theoretical considerations about the physical processes that must occur in the ionosphere and magnetosphere surrounding Jupiter have lead to estimates of the thermal plasma distribution. These models of the Jovian magnetic field and thermal plasma distribution, specify the characteristic plasma and cyclotron frequencies in the magnetosplasma and thereby provide a basis for estimating thelocal electromagnetic and hydromagnetic noise around Jupiter. Spatial analogs of the well-known Clemmow-Mullaly-Allis (CMA) diagrams have been constructed to identify the loci of electron and ion resonances and cutoffs for the different field and plasma models. Regions of reflection, mode coupling, and probable amplification are readily identified. The corresponding radio noise properties may be estimated qualitatively on the basis of these various electromagnetic and hydromagnetic wave mode regions. Frequency bands and regions of intense natural noise may be estimated. On the basis of the models considered, the radio noise properties around Jupiter are quite different from those encountered in the magnetosphere around the Earth. Wave particle interactions are largely confined to the immediate vicinity of the zenographic equatorial plane and guided propagation from one hemisphere to the other apparently does not occur, except for hydromagnetic modes of propagation. The characteristics of these local signals are indicative of the physical processes occurring in the Jovian magnetosphere. Thus, as a remote sensing tool, their observation will be a vital asset in the exploration of Jupiter.     

Alfvén node-free vibrations of white dwarf in the model of solid star with toroidal magnetic field

In the context of white dwarf asteroseismology, we investigate the vibrational properties of a non-convective solid star with an axisymmetric purely toroidal intrinsic magnetic field of two different shapes. Focus is laid on the regime of node-free global Lorentz-force-driven vibrations about the symmetry axis at which material displacements have one and the same form as those for nodeless spheroidal and torsional vibrations restored by Hooke’s force of elastic shear stresses. Particular attention is given to the even-parity poloidal Alfvén modes whose frequency spectra are computed in analytic form, showing how the purely toroidal magnetic fields completely buried beneath the star surface can manifest itself in seismic vibrations of non-magnetic white dwarfs. The spectral formulae obtained are discussed in juxtaposition with those for Alfvén modes in the solid star model with the poloidal, homogeneous internal and dipolar external, magnetic field whose inferences are relevant to Alfvén vibrations in magnetic white dwarfs.     

The periods of stellar models with linked poloidal-toroidal magnetic fields

First-order perturbation theory results for the changes in pulsation frequencies of a Cowling model star containing a magnetic field with both poloidal and toroidal components are presented. A toroidal field large enough to stabilize the poloidal field may reverse the sign of the frequency change caused by a purely poloidal field for some modes, including the fundamental radial mode.     

Equilibrium of self gravitating polytropic cylinders with a magnetic field

The equations of hydromagnetics for a self-gravitating fluid of infinite conductivity are examined in the axisymmetric case in terms of toroidal and poloidal scalars. The stationary state with non-zero poloidal velocity scalar admits and analytical solution for polytropic cylinder of infinite length with a prevalent toroidal magnetic field. The case when the poloidal velocity scalar is zero is also considered.     

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.     

On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < U_c, where U_c is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, U_c is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U^* > U_c is introduced due to the finiteness of the system. When U_c < U < U^*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U^*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.     

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.     

Magnetic deformation of the white dwarf surface structure

The influence of strong, large‐scale magnetic fields on the structure and temperature distribution in white dwarf atmospheres is investigated. Magnetic fields may provide an additional component of pressure support, thus possibly inflating the atmosphere compared to the non‐magnetic case. Since the magnetic forces are not isotropic, atmospheric properties may significantly deviate from spherical symmetry. In this paper the magnetohydrostatic equilibrium is calculated numerically in the radial direction for either for small deviations from different assumptions for the poloidal current distribution. We generally find indication that the scale height of the magnetic white dwarf atmosphere enlarges with magnetic field strength and/or poloidal current strength. This is in qualitative agreement with recent spectropolarimetric observations of Grw+10°8247. Quantitatively, we .nd for e.g. a mean surface poloidal field strength of 100 MG and a toroidal field strength of 2‐10 MG an increase of scale height by a factor of 10. This is indicating that already a small deviation from the initial force‐free dipolar magnetic field may lead to observable effects. We further propose the method of finite elements for the solution of the two‐dimensional magnetohydrostatic equilibrium including radiation transport in the diffusive approximation. We present and discuss preliminary solutions, again indicating on an expansion of the magnetized atmosphere.     

Propagation characteristics of hydromagnetic waves in a cold plasma mixed with a hot plasma and right-hand polarized Pc1 and Pc5

Propagation characteristics of hydromagnetic waves in a cold plasma mixed with a hot plasma under a uniform static magnetic field are investigated. The existence of cold plasma seriously affects the polarization properties of the waves. The results are applied to the interpretation of Pcl and Pc5 with righthand polarizations guided along the geomagnetic field line.     

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.     

Model of polarization state of compressional surface MHD waves in the low-altitude cusp

Examination of thermal plasma data obtained by low-altitude satellite measurements indicates that the intersection of the cusp in the dayside magnetosphere with the topside ionosphere creates a distinct plasma geometry at low altitudes. This region consists of one or two plasma discontinuities with steep boundaries. As a result of the plasma structuring in the cusp which commonly takes place in the winter hemisphere, the propagation of compressional surface MHD waves is supported. This point is illustrated by an analysis of the polarization state of compressional surface MHD waves propagating along a plasma layer with thickness a and ambient magnetic field B₀ parallel to the interfaces. The results obtained are applicable to the case of a single interface, which is derived in the limit a → ∞. In the general case the polarization of the compressional surface MHD waves in the plane transverse to the magnetic field B₀ is elliptical. This feature of the polarization state of the compressional surface modes does not follow from the former analysis by Edwin and Roberts (1982, Solar Phys. 76, 239) for a magnetic slab, because the disturbance components parallel to the interfaces and perpendicular to the magnetic field B₀ have not been examined. Although the absence of these components does not prove to be essential for deriving the exact dispersion equation for arbitrary wave directions of the surface modes, they must be included when considering polarization states. The surface mode polarization in the plasma layer changes its sense three times: at interfaces X = 0 and X = a and in the middle plane X = a/2. For the symmetrical (sausage) mode the wave disturbance component b_n transverse (normal) to the interfaces becomes zero in the middle plane; for the asymmetrical (kink) mode, the component b_t parallel to the interfaces and transverse to the ambient magnetic field is zeroed in the same plane. For a moving observer such as a satellite the polarization patterns which might be recorded change, depending on the velocity of the observer and the angles at which the layered cusp is traversed. An essential feature in the polarization of the compressional surface MHD modes is the presence of jumps in the magnetic disturbance component b_t at the interfaces. These jumps disappear only for propagation along the ambient magnetic field. In this particular case the component b_t vanishes and then the surface modes are undistinguishable from the body modes.     

Effects of the magnetic field model and wave polarisation on the estimation of proton number densities in the magnetosphere using field line resonances

The cold, core plasma mass density in the Earth's magnetosphere may be deduced from the resonant behaviour of ultra-low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) waves. Ground-based magnetometers are the most widely used instruments for recording the signature of ULF wave activity in the magnetosphere. For a suitable model of the background magnetic field and a functional form for the variation of the proton number density with radial distance, the resonant frequencies of ULF waves provide estimates of the equatorial plasma mass density. At high latitudes, the magnetic field model becomes critical when estimating the plasma mass density from FLR data. We show that a dipole field model is generally inadequate for latitudes greater than ∼65° geomagnetic compared with models that are keyed to magnetic activity, interplanetary magnetic field and solar wind properties. Furthermore, the method often relies on the detection of the fundamental ULF resonance, which changes frequency depending on the polarisation of the oscillation. Using idealised toroidal and poloidal oscillation modes, the range of the derived densities as the ULF wave polarisation changes is of the same order as changing the density function from a constant value throughout the magnetosphere to assuming constant Alfven speed in a dipole geometry.     

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.