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.     

Kinetic Alfvén waves on auroral field lines

Several observations near moving arcs require particle acceleration in nonstationary electric fields. We suggest that kinetic Alfvén waves play a significant role in the acceleration process. The characteristic properties of kinetic Alfvén waves are summarized and the Hasegawa and Mima (1976) solitary kinetic Alfvén waves are described. The resonant coupling of large-scale surface waves to the kinetic Alfvén wave is discussed. Finally, we show that kinetic Alfvén waves can reasonably well explain the observations of what has hence been called “electrostatic” shocks.     

The effect of the lower ionosphere on hydromagnetic modes in the plasmasphere

Dimensionless resonant frequencies of hydromagnetic modes have been calculated for a simple model plasmasphere including a lower ionosphere. Results for the Alfvén mode are broadly consistent with those obtained by Hughes and Southwood [1976]. It is further concluded that the lower ionosphere, despite its strong damping effect for part of the day, does not provide much dissipative coupling between adjacent magnetic field shells in the Alfvén mode. The fast mode is found to be only slightly damped for horizontal wavelengths of global extent.     

Torsional Alfvén waves in stratified and expanding magnetic flux tubes

The effects of both density stratification and magnetic field expansion on torsional Alfvén waves in magnetic flux tubes are studied. The frequencies, the period ratio P ₁/P ₂ of the fundamental and its first-overtone, and eigenfunctions of torsional Alfvén modes are obtained. Our numerical results show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional Alfvén waves.     

Compound Effect of Alfvén Waves and Ion-Cyclotron Waves on Heating/Acceleration of Minor Ions via the Pickup Process

A scenario is proposed to explain the preferential heating of minor ions and differential-streaming velocity between minor ions and protons observed in the solar corona and in the solar wind. It is demonstrated by test-particle simulations that minor ions can be nearly fully picked up by intrinsic Alfvén-cyclotron waves observed in the solar wind based on the observed wave energy density. Both high-frequency ion-cyclotron waves and low-frequency Alfvén waves play crucial roles in the pickup process. A minor ion can first gain a high magnetic moment through the resonant wave–particle interaction with ion-cyclotron waves, and then this ion with a large magnetic moment can be trapped by magnetic mirror-like field structures in the presence of the low-frequency Alfvén waves. As a result, the ion is picked up by these Alfvén-cyclotron waves. However, minor ions can only be partially picked up in the corona because of the low wave energy density and low plasma β. During the pickup process, minor ions are stochastically heated and accelerated by Alfvén-cyclotron waves so that they are hotter and flow faster than protons. The compound effect of Alfvén waves and ion-cyclotron waves is important in the heating and acceleration of minor ions. The kinetic properties of minor ions from simulation results are generally consistent with in-situ and remote features observed in the solar wind and solar corona.     

On the role of transition region on the Alfvén wave phase mixing in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of standing Alfvén waves due to phase mixing at the presence of steady flow and sheared magnetic field in the stratified atmosphere of solar spicules. The transition region between chromosphere and corona has also been considered. The initial flow is assumed to be directed along spicule axis, and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that in contrast to propagating Alfvén waves, standing Alfvén waves dissipate in time rather than in space. Density gradients and sheared magnetic fields can enhance damping due to phase mixing. Damping times deduced from our numerical calculations are in good agreement with spicule lifetimes. Since spicules are short living and transient structures, such a fast dissipation mechanism is needed to transport their energy to the corona.     

Flapping motions of the tail plasma sheet induced by the interplanetary magnetic field variations

Flapping motions of the magnetotail with an amplitude of several earth radii are studied by analysing the observations made in the near (x = ?25 ~ ?30 R_E and the distant (x? ?60 R_E) tail regions. It is found that the flapping motions result from fluctuations in the interplanetary magnetic field, especially Alfvénic fluctuations, when the magnitude of the interplanetary magnetic field is larger than ~10 γ and they propagate behind the Earth with the solar wind flow. Flappings tend to be observed in early phases of the magnetospheric substorm, and they have two fundamental modes with periods of ~200 and ~500 sec. In some limited cases a good correspondence with the long period micropulsations (Pc5) in the polar cap region is observed. These observational results are explained by the model in which the Alfvénic fluctuations in the solar wind penetrate into the magnetosphere along the connected interplanetary-magnetospheric field lines. The characteristics of the flapping reveal that the geomagnetic tail is a good resonator for the hydromagnetic disturbances in the solar wind.     

Different eigenproblem models for field line resonances in cold plasma: Effect on magnetospheric density estimates

Magnetospheric plasma density can be remotely sensed through ground-based magnetometer data using a suitable model for field line resonances (FLRs) formed by standing shear Alfvén wave on closed geomagnetic field lines. The simplest type of FLR model, which is also the most relevant for magnetometer data inversion purposes, is based on solving a certain eigenvalue problem. Over the years a number of such models have been developed [Singer, H.J., Southwood, D.J., Walker, R.J., Kivelson, M.G., 1981. Alfvén wave resonances in a realistic magnetospheric magnetic field geometry. J. Geophys. Res. 86, 4589–4596; Rankin, R., Fenrich, F., Tikhonchuk, V.T., 2000. Shear Alfvén waves on stretched magnetic field lines near midnight in Earth's magnetosphere. Geophys. Res. Lett. 27, 3265–3268; Rankin, R., Kabin, K., Marchand, R., 2006. Alfvénic field line resonances in arbitrary magnetic field topology. Adv. Space Res. 38, 1720–1729]. In this paper we summarize the properties of these models and investigate the effect of using these different models on the magnetospheric density inferred from the ground-based magnetometer measurements. We also formulate a simple criterion which can be used to determine which one of these models should be used for a particular field line.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.     

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave–particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfvén waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. In this paper, we assume that i) low-frequency Alfvén and fast waves, emanating from the solar surface, have the same spectral shape and the same amplitude of power spectral density (PSD); ii) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; iii) kinetic wave–particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha–proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfvén-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfvén-cyclotron wave at the same wave propagation angle θ, particularly at 80^°<θ<90^°. When Alfvén-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by a differential speed and a temperature anisotropy of alpha particles via the self-consistently evolving wave–particle interaction. Therefore, fast-cyclotron waves, as a result of linear mode coupling, constitute a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.     

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.     

Wave-trains in the solar wind

Applying an Alfvén-Wave-Extended-QRH-approximation and the method of characteristics, we solve the equations of motion for outwardly propagating Alfvén waves analytically for three different cases of an azimuthal dependence of the background solar wind, (a) for a pure fast-slow stream configuration, (b) for the situation where the high-speed stream originates from a diverging magnetic field region, and (c) for the case of (b) and an initially decreasing density configuration (‘coronal hole’). The reaction of these waves on the background state as well as mode-mode coupling effects are neglected. These three solar wind models are discussed shortly. For the superimposed Alfvén waves we find, on an average, that there is a strong azimuthal dependence of all relevant wave parameters which, correlated with the azimuthal distributions of the solar wind variables, leads to good agreements with observations. The signature of high-speed streams and these correlations could clearly indicate solar wind streams originating from ‘coronal holes’. Contrary to the purely radial dependent solar wind, where outwardly propagating Alfvén waves are exclusively refracted towards the radial direction, we now find a refraction nearly perpendicular to the direction of the interplanetary magnetic field in the compression region and closely towards the magnetic field direction down the trailing edge and in the low-speed regime.     

Time-Distance Seismology and the Solar Transition Region

Time-Distance ‘travel time’ perturbations (as inferred from wave phase) are calculated relative to the quiet-Sun as a function of wave orientation and field inclination in a uniform inclined magnetic field. Modelling indicates that the chromosphere-corona Transition Region (TR) profoundly alters travel times at inclinations from the vertical θ for which the ramp-reduced acoustic cutoff frequency ω _c cosθ is similar to the wave frequency ω. At smaller inclinations phase shifts are much smaller as the waves are largely reflected before reaching the TR. At larger inclinations, the shifts resume their quiet-Sun values, although with some resonant oscillatory behaviour. Changing the height of the TR in the model atmosphere has some effect, but the thickness and temperature jump do not change the results substantially. There is a strong correspondence between travel-time shifts and the Alfvén flux that emerges at the top of the modelled region as a result of fast/Alfvén mode conversion. We confirm that the TR transmission coefficient for Alfvén waves generated by mode conversion in the chromosphere is far larger (typically 30 % or more) than for Alfvén waves injected from the photosphere.     

Decay instability of kinetic Alfvén waves in preflare plasmas of the loops in active solar regions

We examine the physical conditions for the origin of the decay instability of kinetic Alfvén waves in loop plasmas at the early flare stages. The synchronism conditions are used to derive a modified expression for the nonlinear growth rate of the process of the decay of the primary kinetic Alfvén wave (KAW) into an ion-acoustic wave and a secondary KAW. The threshold amplitude of the primary KAW is calculated in units of the background magnetic field strength in the chromospheric section of loop current circuit.     

Phase mixing of standing Alfvén waves with shear flows in solar spicules

Alfvénic waves are thought to play an important role in coronal heating and solar wind acceleration. Here we investigate the dissipation of such waves due to phase mixing at the presence of shear flow and field in the stratified atmosphere of solar spicules. The initial flow is assumed to be directed along spicule axis and to vary linearly in the x direction and the equilibrium magnetic field is taken 2-dimensional and divergence-free. It is determined that the shear flow and field can fasten the damping of standing Alfvén waves. In spite of propagating Alfvén waves, standing Alfvén waves in Solar spicules dissipate in a few periods. As height increases, the perturbed velocity amplitude does increase in contrast to the behavior of perturbed magnetic field. Moreover, it should be emphasized that the stratification due to gravity, shear flow and field are the facts that should be considered in MHD models in spicules.     

Parametric generation of acoustic-gravity waves by Alfvén waves in the solar atmosphere

Based on a plane-parallel isothermal model solar atmosphere permeated by a uniform magnetic field directed against the action of gravity, we investigate the parametric generation of acoustic-gravity disturbances by Alfvén waves propagating along the corresponding field lines. We established that for a weak linear coupling of Alfvén waves, the nonlinear interaction of Alfvén waves propagating in opposite directions (rather than in the same direction) is the predominant generation mechanism of acoustic-gravity disturbances at the difference frequency. In this case, no acoustic flow (wind) was found to emerge at a zero difference frequency in the acoustic-gravity field.     

Transfer of Energy, Potential, and Current by Alfvén Waves in Solar Flares

Alfvén waves play three related roles in the impulsive phase of a solar flare: they transport energy from a generator region to an acceleration region; they map the cross-field potential (associated with the driven energy release) from the generator region onto the acceleration region; and within the acceleration region they damp by setting up a parallel electric field that accelerates electrons and transfers the wave energy to them. The Alfvén waves may also be regarded as setting up new closed-current loops, with field-aligned currents that close across field lines at boundaries. A model is developed for large-amplitude Alfvén waves that shows how Alfvén waves play these roles in solar flares. A picket-fence structure for the current flow is incorporated into the model to account for the “number problem” and the energy of the accelerated electrons.     

Reflection of Alfvén waves by non-uniform ionospheres

Magnetospheric Alfvén waves are reflected by the ionosphere. We investigate the effect of horizontally varying ionospheric conductivity on the process of Alfvén wave reflection. Four idealised ionospheric models are considered in detail. We find that the reflection process is strongly dependent on the orientation of the wave electric field vector with respect to the boundary between high and low conductivities, and under certain conditions subsidiary Alfvén waves are generated. The field-aligned currents in the subsidiary Alfvén waves serve to close divergent horizontal currents resulting from the non-uniform ionospheric conductivity. The implications for ground-based pulsation studies are discussed.     

Incompressible MHD Turbulence

The inertial range of incompressible MHD turbulence is most conveniently described in terms of counter propagating waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves. MHD turbulence is anisotropic with energy cascading more rapidly along k _⊥ than along k _∥. Anisotropy increases with k _⊥ such that the excited modes are confined inside a cone bounded by k _∥∝ k _perp ^2/3. The opening angle of the cone, θ(k _⊥)∝ k _⊥ ^-1/3, defines the scale dependent anisotropy. MHD turbulence is generically strong in the sense that the waves which comprise it are critically damped. Nevertheless, deep inside the inertial range, turbulent fluctuations are small. Their energy density is less than that of the background field by a factor θ²(k _⊥)≪. MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating wave packets. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The former exceeds the latter by θ^-1(k _⊥)≫ 1 which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.