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.     

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.     

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.     

Observations of Pg pulsations in the Northern Auroral zone and at lower latitude conjugate regions

An analysis is made of giant pulsation (Pg) data recorded at ground stations in the Northern Auroral Zone in Scandanavia (mainly at Tromsø, L = 6.4 and Kiruna, L = 5.5) during the period September 1976 to December 1977. They are shown to have a meridional variation of amplitude and polarization consistent with a field line resonance structure and their vertical component behaviour suggests that they also have a rapid azimuthal phase variation. Limited data from conjugate stations at L = 4.4 are used to show that Pg's are odd mode oscillations of the field line. Pg's are equated to the observation of a unique compressional wave in space at synchronous orbit and it is suggested that they result from the drift wave instability of the compressional Alfven wave at the outer edge of the quiet time ring current.     

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.     

Global Pc5 wave activity observed using SuperDARN radars and ground magnetometers during an extended period of northward IMF

Observations are presented of long-lived global Pc5 ULF wave activity observed at a wide range of local times. The event was monitored in the high latitude ionosphere (∼60–80° magnetic latitude) by several SuperDARN HF radars and 5 magnetometer chains in Scandinavia, Greenland, Canada, Alaska and Russia. The event coincided with a protracted period (∼36 h) of northward interplanetary magnetic field (IMF). The study focuses on 4 h during which distinct dawn/dusk asymmetries in the wave characteristics were observed with multiple field line resonance (FLR) structures observed in the dawn flank at 1.7, 2.6, 3.3, 4.2 and 5.4 mHz and compressional oscillations in the dusk flank at 1.7 and 2.3 mHz. The data indicated an anti-sunward propagation in both the dawn and dusk flanks and a low azimuthal m number (∣m∣∼6) suggesting a generation mechanism external to the Earth's magnetosphere. A sudden increase in the solar wind dynamic pressure followed by a period of strongly northward, B_z dominated IMF, coincides with the observations and also a large increase in Pc5 wave power observed in the dawn flank. The observed enhancements in the wave activity and FLR structures are thought to be due to a Kelvin–Helmholtz driven waveguide mode. Additionally, there is no evidence that the frequencies of the FLRs are intrinsic to the solar wind. It thus seems that the frequencies were determined by the dimensions of the magnetospheric cavity.     

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.     

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.     

Spectral studies of geomagnetic pulsations with periods between 20 and 120 sec,and their relationship to the plasmapause region

Digital spectrograms have been computed for 18 days of geomagnetic pulsation activity at three UK Earth current stations (L = 2.6?3.6).Three main conclusions are drawn: (1) There are days when the period of the dominant spectral amplitude is ordered according to the observatory latitude. The most frequently observed large amplitude spectral peaks are centred on 80, 60 and 45s for South Uist (L = 3.6), Eskdalemuir (L = 3.1) and East Anglia (L = 2.6). respectively. (2) There are other days when the period of the dominant spectral amplitude is the same at all the observatories. (3) When Pc 3 and 4 period waves have been detected together, the latitude dependence of the amplitudes supports the theory that the shorter period pulsation is enhanced in the plasmatrough while the longer period wave is enhanced within the plasmasphere.     

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.     

Diffuse auroral precipitation in the jovian upper atmosphere and magnetospheric electron flux variability

The deposition of energetic electrons in Jupiter's upper atmosphere provides a means, via auroral observations, of monitoring electron and plasma wave activity within the magnetosphere. Not only does particle precipitation indicate a potential change in atmospheric chemistry, it allows for the study of episodic, pronounced flux enhancements in the energetic electron population. A study has been made of the effects of such electron injections into the jovian magnetosphere and of their ability to provide the source population for variations in diffuse auroral emissions. To identify the source region of precipitating auroral electrons, we have investigated the pitch-angle distributions of high-resolution Galileo Energetic Particle Detector (EPD) data that indicate strong flux levels near the loss cone. The equatorial source region of precipitating electrons has been determined from the locations of Galileo's in situ measurements by tracing magnetic field lines using the KK97 model. The primary source region for Jupiter's diffuse aurora appears to lie in the magnetic equator at 15-40 RJ, with the predominant contribution to precipitation flux (tens of ergs cm⁻² s⁻¹ sr⁻¹) stemming from <30 RJ. Variability of flux for energetic electrons in this region is also important to the irradiation of surfaces and atmospheres for the Galilean moons: Europa, Ganymede, and Callisto. The average diffuse auroral precipitation flux has been shown to vary by as much as a factor of six at a given radial location. This variability appears to be associated with electron injection events that have been identified in high-resolution Galileo EPD data. These electron flux enhancements are also associated with increased whistler-mode wave activity and magnetic field perturbations, as detected by the Galileo Plasma Wave Subsystem (PWS) and Magnetometer (MAG), respectively. Resonant interactions with the whistler-mode waves cause electron pitch-angle scattering and lead to pitch-angle isotropization and precipitation.     

Multipoint observations of low latitude ULF Pc3 waves in south-east Australia

Geomagnetic pulsations recorded on the ground are the signatures of the integrated signals from the magnetosphere. Pc3 geomagnetic pulsations are quasi-sinusoidal variations in the earth’s magnetic field in the period range 10–45 seconds. The magnitude of these pulsations ranges from fraction of a nT (nano Tesla) to several nT. These pulsations can be observed in a number of ways. However, the application of ground-based magnetometer arrays has proven to be one of the most successful methods of studying the spatial structure of hydromagnetic waves in the earth’s magnetosphere. The solar wind provides the energy for the earth’s magnetospheric processes. Pc3–5 geomagnetic pulsations can be generated either externally or internally with respect to the magnetosphere. The Pc3 studies undertaken in the past have been confined to middle and high latitudes. The spatial and temporal variations observed in Pc3 occurrence are of vital importance because they provide evidence which can be directly related to wave generation mechanisms both inside and external to the magnetosphere. At low latitudes (L < 3) wave energy predominates in the Pc3 band and the spatial characteristics of these pulsations have received little attention in the past. An array of four low latitude induction coil magnetometers were established in south-east Australia over a longitudinal range of 17 degrees at L = 1.8 to 2.7 for carrying out the study of the effect of the solar wind velocity on these pulsations. Digital dynamic spectra showing Pc3 pulsation activity over a period of about six months have been used to evaluate Pc3 pulsation occurrence. Pc3 occurrence probability at low latitudes has been found to be dominant for the solar wind velocity in the range 400–700 km/s. The results suggest that solar wind controls Pc3 occurrence through a mechanism in which Pc3 wave energy is convected through the magnetosheath and coupled to the standing oscillations of magnetospheric field lines.     

Meridional characteristics of a Pc 4 micropulsation event in the plasmasphere

An analysis was made of a complex large amplitude Pc 4 micropulsation, of four hours duration around local noon, observed at five ground stations in the United Kingdom (2.4? L ?3.8). The final pulsation waveform was shown to be the results of the superposition of wave packets of different periods. The meridional variation of the amplitude of the different period wavepackets was consistent with their being fundamental “toroidal” field line resonances within the plasmasphere, rotated through 90° in their transmission through the ionosphere in accordance with recent theoretical predictions. Other predicted ionospheric effects, such as the loss of the sense-of-polarization reversal across the amplitude maximum, were apparent in the meridional variation of the polarization characteristics.     

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.     

Modelling of Pc5 pulsation structure in the magnetosphere

Magnetohydrodynamic resonance theory is used to model the structure of the magnetospheric and ionospheric electric and magnetic fields associated with Pc5 geomagnetic pulsations. In this paper the variation of the fields across the invariant latitude of the resonance are computed. The results are combined with calculations of the variation along a field line to map the fields down to the ionosphere. In one case the results are compared with measurements obtained by the STARE auroral radar and show good agreement. The relationship between the width of the resonance region and ionospheric height-integrated Pedersen conductivity is computed and it is shown how auroral radar measurements of Pc5 oscillations could be used to determine ionospheric height-integrated Pedersen conductivity. It is pointed out that from these calculations it would be possible to identify the field line on which a satellite was located by comparing a Pc5 pulsation observed by the satellite, and the same pulsation observed by STARE.     

Pc5 pulsations associated with ring current proton drifts: Stare radar observations

Detailed properties of a Pc5 pulsation with large azimuthal wavenumber observed using the STARE radar have recently been reported. A further four examples of this type of pulsation are presented, and it is shown that their properties are generally similar to those of the first example. However, there are some differences, the most important being that the variation of azimuthal phase velocity with latitude is significantly different for different time intervals during individual events, so that a mean phase velocity for a given latitude cannot be defined.When mapped to the equatorial plane in a dipole geomagnetic field, the variation of azimuthal phase velocity with L resembles the gradient-curvature drift of energetic protons in only a few time intervals within the events. The results are interpreted in terms of current theories of drift and bounce resonance of energetic particles with hydromagnetic waves. It is found that no single theory explains all aspects of the observations.     

Magnetically distorted polytropes

The oscillations of a gaseous polytrope with a magnetic field having both a toroidal and a poloidal component are examined using the second-order tensor virial equations on the assumption that the magnetic energy is small compared with the gravitational energy. The frequencies of oscillation of the transverse shear, the toroidal and the coupled pulsation modes are tabulated for polytropic indicesn=1, 1.5, 2, 3 and 3.5. It is found that the magnetic field decreases the frequency of oscillation of (i) the transverse shear mode and (ii) the mode which starts as a radial pulsation in the absence of a magnetic field while it increases the frequency of oscillation of (i) the toroidal mode and (ii) the Kelvin mode. In all cases the shift in frequency decreases with increasingn.     

Hydromagnetic waves in structured magnetic fields

Although the inhomogeneous nature of solar magnetic fields is now well established, most theoretical analyses of hydromagnetic wave propagation assume infinite homogeneous fields. Here we reformulate the hydromagnetic wave problem for magnetic fields which vary in one direction perpendicular to the field. The permitted modes of small amplitude hydromagnetic oscillations are considered, first in the case of a single interface between semi-infinite magnetic and non-magnetic compressible regions, and secondly for a magnetic flux sheath of given thickness imbedded in a nonmagnetic region. It is shown that, for small values of R (the ratio of the Alfvén to the sound speed), an acoustic or p-mode wave front passes through the flux sheath with only minor deformation. However, for large R, the transmitted acoustic wave is attenuated and, depending upon the thickness of the flux sheath and the angle of incidence, a hydromagnetic wave may be effectively trapped and guided along the flux sheath. It is also shown that, for the symmetric vibration of the flux sheath in the absence of incident acoustic waves, only slow mode type waves are permitted. Thus, in compressible regions for which R > 1 the Alfvénic-type fast mode is not a permitted mode of free vibration of a flux sheath.     

Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave–plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectrum changes mostly at the distances before ～?20 R _⊙. Further into the heliosphere, the electron flux spectrum of electrons forms a broken power law relatively similar to what is observed at 1 AU.