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.     

Localised compressional hydromagnetic waves in the magnetospheric ring current

It is shown that the field line resonance phenomenon that occurs for quasi-transverse signals in a non-uniform cold plasma generally occurs for disturbances with a compressional magnetic component in a hot plasma like the ring current. The equations describing such localised signals are derived and discussed in various limits. It is pointed out that recent observations of low frequency compressional oscillations on spacecraft may be an example of such localised signals.     

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.     

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.     

Nonlinear coupling between electromagnetic fields in a strongly magnetized electron-positron plasma

The nonlinear coupling between electromagnetic fields in a strongly magnetized electron-positron plasma is considered. We point out that compressional magnetic field perturbations are excited by the rotational part of the nonlinear current, and derive a new nonlinear system of equations that is basic for studies of modulational instabilities and coherent nonlinear structures in magnetized electron-positron plasmas.     

Interaction of energetic particles with HM-waves in the magnetosphere

Energetic particle response in electromagnetic fields of ULF HM-waves in the magnetosphere is reviewed. Pc4–5 geomagnetic pulsations observed at the synchronous altitude are classified into three types, in respect to their major magnetic field polarization in different directions, local time dependence, and different characteristics of accompanied flux modulations of energetic particles, i.e., two nearly transverse waves with the azimuthal and the radial polarization, and the compressional stormtime pulsations. Firstly, we formulate the drift kinetic theory of particle flux modulations under the constraint of the magnetic moment conservation. A generalized energy integral of the particle motion interacting with a ULF-wave with the three-dimensional structure propagating to the azimuthal direction is obtained in the L-shell coordinate of a mirror magnetic field. Its linearized form is reduced to the same form as the previously derived energy change, including the bounce-drift resonant interaction. It is shown that the perturbed guiding center distribution function of energetic particles consists of four contributions, the adiabatic mirror effect corresponding to pitch-angle change, the kinetic effects due to energy change and the accompanying L-shell displacement, and the bounceaveraged drift phase bunching. Secondly, the basic HM-wave modes constitutingcoupling ULF oscillations in non-uniform plasmas are discussed in different models of approach for different plasma states. The diamagnetic drift Alfvén wave and the compressional drift wave with a larger azimuthal mode number in a high-beta plasma are candidates for the stormtimes pulsations. The former is intrinsically a guided localized mode, while the latter is a non-localized mode. By making use of the above preparation, we apply the developed drift kinetic theory to interpret the phase relationships between the ion flux modulation and the geomagnetic pulsation in some selected examples of observations, demonstrating a fair agreement in theoretical results with the observations.     

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 compressional Pc4 pulsation observed by three satellites in geostationary orbit near local midnight

We describe the observation of a magnetic pulsation with a period of 55 s, recorded at geostationary orbit by three satellites (ATS 6, SMS 1 and SMS 2) in the local time sector 2100–2400. We use magnetic data from all three spacecraft and also plasma data from ATS 6. The pulsation had a large compressional magnetic component which appeared to be balanced by pressure fluctuations in the hot ring current plasma which were in antiphase with the magnetic variations. This allows the wave to be guided along a field line. From the plasma data we are also able to obtain estimates of the field line displacement and hence the electric field, which enables us to conclude that this is a second harmonic field line resonance. We find that the wave has a very short East-West (E-W) wavelength (m?100) and a westward azimuthal group velocity of about 30 km s^?1. The most probable source for this wave is a bounce resonant interaction with ring current protons. The characteristics of this wave are in many ways similar to those of giant pulsations observed on the ground. ATS 6 was near the inner edge of the ring current electrons and as the wave converted the 10 keV electron Alfvén layer back and forth across ATS 6, we were able to estimate the Alfvén layer energy gradient and obtain a value of 1 keV in 1000 km. This gradient is considerably steeper than that predicted by a steady uniform convection electric field.     

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfvén mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.     

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.     

Venus Express observations of ULF and ELF waves in the Venus ionosphere: Wave properties and sources

Electrical activity in a planetary atmosphere enables chemical reactions that are not possible under conditions of local thermodynamic equilibrium. In both the Venus and terrestrial atmospheres, lightning forms nitric oxide. Despite the existence of an inventory of NO at Venus like the Earth’s, and despite observations of the signals expected from lightning at optical, VLF, and ELF frequencies, the existence of Venus lightning still is met with some skepticism. The Venus Express mission was equipped with a fluxgate magnetometer gradiometer system sampling at rates as high as 128 Hz, and making measurements as low as 200 km altitude above the north polar regions of Venus. However, significant noise levels are present on the Venus Express spacecraft. Cleaning techniques have been developed to remove spacecraft interference at DC, ULF, and ELF frequencies, revealing two types of electromagnetic waves, a transverse right-handed guided mode, and a linearly polarized compressional mode. The propagation of both types of signals is sensitive to the magnetic field in ways consistent with propagation from a distant source to the spacecraft. The linearly polarized compressional waves generally are at lower frequencies than the right-handed transverse waves. They appear to be crossing the usually horizontal magnetic field. At higher frequencies above the lower hybrid frequency, waves cannot enter the ionosphere from below when the field is horizontal. The arrival of signals at the spacecraft is controlled by the orientation of the magnetic field. When the field dips into the atmosphere, the higher frequency guided mode above the lower hybrid frequency can enter the ionosphere by propagating along the magnetic field in the whistler mode. These properties are illustrated with examples from five orbits during Venus Express’ first year in orbit. These properties observed are consistent with the linearly polarized compressional waves being produced at the solar wind interface and the transverse guided waves being produced in the atmosphere.     

Observations of a quiet-time Pc5 wave in the outer magnetosphere

We report an observation of the radial profile of a Pc5 magnetic pulsation and the associated energetic electron flux oscillations from 10 to 18 Re, recorded by the IMP-5 satellite at 19.00 M.L.T. on 21 March 1970. The Pc5 pulsation was mainly compressional and occurred during extremely quiet geomagnetic conditions. Fluxes of energetic electrons detected above three energy thresholds (18, 45, and 80 keV) were found to oscillate out of phase with magnetic field intensity. One new result is that both the wave amplitude and the wave period increased with radial distance. Second, the electron flux oscillation amplitude was roughly proportional to magnetic field fluctuation amplitude and wave period. The wave event is found to be interpreted better as an ion drift wave because of lack of polarization reversal. The characteristics of energetic electron flux oscillations are shown to agree qualitatively with theoretical calculations of the kinetic perturbation of distribution functions by compressional waves.     

Drift anisotropy instability of a finite-β magnetospheric plasma

A unified theory of low frequency instabilities in a two component (cold and hot) finite-β magnetospheric plasma is suggested. It is shown that the low frequency oscillations comprise two wave modes : compressional Alfvén and drift mirror mode. No significant coupling between them is found in the long-wave approximation. Instabilities due to spontaneous excitation of these oscillations are considered. It is found that the temperature anisotropy significantly influences the instability growth rate at low frequency. A new instability due to the temperature anisotropy and density gradient appears when the frequency of compressional Alfvén waves is close to the drift mirror mode frequency. The theoretical predictions are compared in detail with the Pc5 event of 27 October 1978 observed simultaneously by the GEOS 2 satellite and the STARE radar facility. It is shown that the experimental results can be interpreted in terms of a compressional Alfvén wave driven by the drift anisotropy instability.     

Pc3-4 geomagnetic pulsations at very low latitude in Brazil

In order to investigate Pc3-4 geomagnetic pulsations at very low and equatorial latitudes, L=1.0 to 1.2, we analyzed simultaneous geomagnetic data from Brazilian stations for 26 days during October-November 1994. The multitaper spectral method based on Fourier transform and singular value decomposition was used to obtain pulsation power spectra, polarization parameters and phase. Eighty-one (81) simultaneous highly polarized Pc3-4 events occurring mainly during daytime were selected for the study. The diurnal events showed enhancement in the polarized power density of about 3.2 times for pulsations observed at stations close to the magnetic equator in comparison to the more distant ones. The phase of pulsation observed at stations near the magnetic equator showed a delay of 48-62° in relation to the most distant one. The peculiarities shown by these Pc3-4 pulsations close to the dip equator are attributed to the increase of the ionospheric conductivity and the intensification of the equatorial electrojet during daytime that regulates the propagation of compressional waves generated in the foreshock region and transmitted to the magnetosphere and ionosphere at low latitudes. The source mechanism of these compressional Pc3-4 modes may be the compressional global mode or the trapped fast mode in the plasmasphere driving forced field line oscillations at very low and equatorial latitudes.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

Self-gravitational instability in magnetized finitely conducting viscoelastic fluid

The linear self-gravitational instability of finitely conducting, magnetized viscoelastic fluid is investigated using the modified generalized hydrodynamic (GH) model. A general dispersion relation is obtained with the help of linearized perturbation equations using the normal mode analysis and it is discussed for longitudinal and transverse modes of propagation. In longitudinal propagation, we find that Alfven mode is uncoupled with the gravitating mode. The Jeans criterion of instability is determined which depends upon shear viscosity and bulk viscosity while it is independent of magnetic field. The viscoelastic effects modify the fundamental Jeans criterion of gravitational instability. In transverse mode of propagation, the Alfven mode couples with the acoustic mode, compressional viscoelastic mode and gravitating mode. The growth rate of Jeans instability is compared in weakly coupled plasma (WCP) and strongly coupled plasma (SCP) which is larger for SCP in both the modes of propagations. The presence of finite electrical resistivity removes the effect of magnetic field in the condition of Jeans instability and expression of critical Jeans wavenumber. It is found that Mach number and shear viscosity has stabilizing while finite electrical resistivity has destabilizing influence on the growth rate of Jeans instability.     

Excess heating of corona and chromosphere above magnetic regions by non-linear Alfvén waves

Excess heating of the active region solar atmosphere is interpreted by the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction of this large flux is propagated out to the corona, and a large velocity amplitude exceeding the local Alfvén velocity is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves gets involved in such a case with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formulation for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alvén waves will eventually be thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of thus produced slow-mode waves may provide means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, with higher density as a consequence of increased scale height, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature of the general corona) may be explained in a natural fashion.     

Some observed characteristics of solar radar echoes and their implications

The results of a series of radar studies of the sun at 38.2 MHz are presented. The echoes imply ever-present compressional waves in the corona, and these waves are likely associated with coronal heating. Some echoes are refracted by plasma clouds high in the corona. Other echoes are reflected by dense plasma irregularities moving outward very slowly at 0 to 20 km/sec. These are sometimes found as far out as three solar radii from the sun's center. Suggestions for future solar radar experiments and the need for them are outlined.     

Cluster observations of Pc 1–2 waves and associated ion distributions during the October and November 2003 magnetic storms

Unusual wave activity in the Pc 1–2 frequency band (0.1–5 Hz) was observed by the Cluster spacecraft in association with the two large geomagnetic storms of late 2003. During the onset of the Hallowe’en storm on October 29, 2003, intense broadband activity between ∼0.1 and 0.6 Hz appeared at all 4 spacecraft on both sides of the magnetic equator at perigee (near 1400 UT and 08:45 MLT). Power was especially strong and more structured in frequency in the compressional component: a minimum in wave power was observed at 0.38 Hz, corresponding to the oxygen ion cyclotron frequency. Poynting vector calculations indicated that wave power was primarily directed radially inward rather than along the magnetic field. Narrowband purely compressional waves near 0.15 Hz appeared at higher dayside latitudes in the southern hemisphere. CIS ion spectrometer data during this pass revealed that O⁺ was the dominant energetic ion. During the recovery phase of the November storm, on November 22, 2003, predominantly transverse 1.8 Hz waves with peak-to-peak amplitude of 10 nT were observed by all four spacecraft near perigee at L=4.4. During this more typical Pc 1 event, wave power was directed along B, toward the northern ionosphere. An unusually polarized 2.3 Hz emission (with power in the radial and compressional, but not azimuthal directions) was observed at L=5.4–5.9, 10–15° south of the magnetic equator. We infer that this wave event may have been generated on lower L shells and propagated obliquely to Cluster's location. Consistent with other recent observations, anisotropic plasma sheet/ring current proton distributions appeared to be a necessary condition for occurrence of waves during both passes, but was not always a sufficient condition. The transverse waves of November 22 occurred in regions which also contained greatly increased fluxes of cool ions (E<1 keV). On both days, Cluster observed features not previously reported, and we note that the purely compressional nature of the October 29 events was not anticipated in previous theoretical studies. The fact that these unusually polarized waves occurred in association with very intense geomagnetic storms suggests that they are likely to be extremely rare.     

Features of the Martian Magnetic Field Structure

Based on the single-fluid MHD model of Mars space simulation, this paper has studied the magnetic field structure in the near-Mars space and investigated the influence of Martian crustal magnetic anomalies on the magnetic field structure. In the process of the solar wind interaction with Mars, the bow shock and magnetic pile-up region are produced. The interplanetary magnetic lines are curved and deformed while they are towed toward the two poles by the solar wind. The majority of magnetic lines bypass the two poles, then leave behind a ‘V-shaped’ structure in the magnetotail behind Mars. In the crust of Mars, the local magnetic anomalies have a noticeable influence on the magnetic field structure. The magnetic anomalies at different positions and in different intensities interact with the solar wind to form the mini-magnetospheres of different structures and morphologies, such as the towed mini-magnetosphere and the mini-magnetosphere with open magnetic lines. The local magnetic anomalies have changed the near-Mars magnetic field structure, and probably changed the plasma distribution as well.