Compressional MHD Waves Research Articles

Spatial damping of MHD waves in solar prominences: Effect of background flow

The extensive arch-shaped features, solar prominences, are observed subtending high into the solar corona. Considering the prominences to be unbound, homogeneous and isothermal, invoking the background flow, in presence of the Newtonian radiation and turbulent viscosity, to investigate the spatial damping of compressional MHD waves, we derived a dispersion relation and solved it numerically for both the Kraichnan and Kolmogorov turbulences for a time span of 10 - 5 s to 10 5 s. For Kraichnan and Kolmogorov turbulences, we investigated the effect of background flow as well as variable physical parameters (e.g. electron density, magnetic field and angle between propagation vector and magnetic field) on the damping length of fast and slow modes. Our findings reveal that the background flow does not show any Doppler shift in the damping length of Fast as well as Slow modes for shorter periods. However, for the longer periods, the fast modes show significantly smaller Doppler shift but interestingly, we noticed that the slow modes exhibit a substantial Doppler shift.

Amplification of compressional magnetohydrodynamic waves in systems with forced entropy oscillations

The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance. In addition, it is shown that the considered waves are mutually coupled as a consequence of the nonequilibrium state of the background medium. The coupling is strongest when the plasma beta approximately 1 . The proposed formalism is sufficiently general and can be applied to many dynamical systems, both under terrestrial and astrophysical conditions.

Spatial damping of compressional MHD waves in prominences

Aims. We study the spatial damping of linear compressional MHD waves in a homogeneous, isothermal, and unbounded prominence. Methods. We derive a general dispersion relation invoking the Newtonian radiation and turbulent viscosity. The turbulent viscosity is derived from SUMER and CDS observations for Kraichnan and Kolmogorov turbulences. Since we are interested in the spatial damping, the dispersion relation is solved numerically considering ω as real and k as complex corresponding to slow, fast, and thermal modes. Results. Both the slow and fast modes show strong damping, but the thermal mode is absent. The turbulent viscosity derived from observations can be a viable mechanism for the spatial damping of slow and fast modes. For a wave period of 1 s, the damping length for slow and fast modes is found to be $1.1 \times 10^{2}$ km for the Kolmogorov turbulence. Correspondingly, the damping length of slow modes is $1.3 \times 10^{1}$ km and for fast modes $1.9\times 10^{2}$ km for the Kraichnan turbulence. From the damping length study of slow modes, it is found that Kraichnan turbulence dominates for short wave periods between 10 -7 to 10 2 s, and the Kolmogorov turbulence dominates for longer wave periods between 10 3 to 10 5 s. From the damping length of fast modes, it is found that the Kraichnan turbulence dominates from very short to long wave periods. Conclusions. The Kraichnan and Kolmogorov turbulence can be a viable damping mechanism for the spatial damping of short-period oscillations. In particular, the short-period oscillations (5-15 min) observed in quiescent limb prominences, which seem to be due to internal fundamental slow modes, have damping lengths in the range $1.9{-}3.7\times 10^{3}$ km for Kolmogorov turbulence and $3.5 \times 10^{3}{-}3.1 \times 10^{4}$ km for Kraichnan turbulence. Correspondingly, for fast modes, the damping length is in the range $2.6\times 10^{5}{-}2.3\times 10^{6}$ km for Kolmogorov turbulence and $1.7 \times 10^{7}{-}1.5\times 10^{8}$ km for Kraichnan turbulence. This study underlines the importance of turbulent viscosity for explaining the damping of both slow and fast modes, which, hitherto, has not been explored.

Test particle simulation of the Electron Firehose instability

In the course of the energization of electrons to energies of some tens of keV during the impulsive phase of a solar flare, the velocity distribution function of the electrons is predicted to become anisotropic with (Here, and denote directions with respect to the background magnetic field). Such a configuration can become unstable to the so-called Electron Firehose instability (EFI). Left hand circularly polarized electromagnetic waves propagating along the magnetic field are excited via a non-resonant mechanism: electrons non-resonantly excite the waves while the protons are in resonance and carry the wave. The non-resonant nature of the instability raises the question of the response of the electron population to the growing waves. Test particle simulations are carried out to investigate the pitch-angle development of electrons injected to single waves and wave spectra. To interpret the simulation results, a drift kinetic approach is developed. The findings in the case of single wave simulations show the scattering to larger pitch-angles in excellent agreement with the theory. The situation dramatically changes when assuming a spectrum of waves. Stochasticity is detected at small initial parallel velocities resulting in significant deviations from drift kinetic theory. It enhances the scattering rate of electrons with initial parallel velocity below to the mean thermal perpendicular velocity. Increased scattering is also noticed for electrons having initial parallel velocity within an order of magnitude of the resonance velocity. The resulting pitch-angle scattering is proposed to be an important ingredient in Fermi-type electron acceleration models, particularly transit-time acceleration by compressional MHD waves.

Signatures of mode conversion and kinetic Alfvén waves at the magnetopause

It has been suggested that resonant mode conversion of compressional MHD waves into kinetic Alfvén waves at the magnetopause can explain the abrupt transition in wave polarization from compressional to transverse commonly observed during magnetopause crossings [Johnson and Cheng, 1997b]. We analyze magnetic field data for magnetopause crossings as a function of magnetic shear angle (defined as the angle between the magnetic fields in the magnetosheath and magnetosphere) and compare with the theory of resonant mode conversion. The data suggest that amplification in the transverse magnetic field component at the magnetopause is not significant up to a threshold magnetic shear angle. Above the threshold angle significant amplification results but with weak dependence on magnetic shear angle. Waves with higher frequency are less amplified and have a higher threshold angle. These observations are qualitatively consistent with theoretical results obtained from the kinetic‐fluid wave equations.

A three-dimensional model of the propagation of Alfvén waves through the auroral ionosphere: first results

The propagation of Alfvén waves in the auroral ionosphere is important in the determination of ground signatures of time-varying currents, in the formation of Pc1 compressional waves that can be ducted in the ionospheric waveguide, and in the development of field-aligned currents and parallel electric fields during auroral acceleration processes. This report presents the first results from a three-dimensional model of the linear propagation of these waves. In this model, the ionosphere is treated as a thin slab carrying Pedersen and Hall currents. The jump conditions across this boundary lead to the coupling of shear and compressional MHD modes at the ionosphere and also allow the ground signatures of these waves to be calculated within the context of the model. This model has been used to study this coupling and to illustrate the excitation and propagation of compressional MHD waves within the ionospheric waveguide. A new numerical scheme for the modeling of parallel electric fields is introduced and the excitation of resonance cone structures by narrow impulses is demonstrated.

Compressional MHD waves in the magnetosphere: A new approach

Dynamics of compressional MHD wave propagation is theoretically studied in the dayside and nightside magnetosphere. In order to analytically examine the MHD wave equation, we adopt the quantum mechanical approach which is often used in the problem of the Schrödinger's equation. The wave solutions are obtained for dayside and nightside Alfven speed profiles, respectively, without any arbitrary boundary condition at the magnetopause or the bow shock. The result shows that the previous cavity/waveguide models are found to be inappropriate for studying compressional wave properties in the magnetosphere. We discuss the role of virtual resonances which generally represent any possible compressional modes in the magnetosphere.

MHD wave characteristics inferred from correlations between X-rays, VLF, and ULFs at Syowa Station, Antarctica and Tjörnes, Iceland (L∼6)

The Polar Patrol Balloon No. 6 (PPB#6) observed quasi-periodic pulsations of bremsstrahlung X-rays (E 30∼120 keV) in the daytime of 0855 UT (0914 MLT) ∼ 1630 UT (1614 MLT) on January 5, 1993, near Syowa Station, Antarctica (L∼6). The X-ray pulsations near the noon (1208:00 UT (1216 MLT) ∼ 1225:04 UT (1232 MLT)) include a period of about 260 sec, which corresponds to Pc 5 magnetic pulsations. It was found that at Syowa Station and Tjornes, Iceland, which are both pair locations of the geomagnetic conjugacy, the X-ray pulsations are in correlation with the ULF-D pulsations. Also the Tjornes VLF (2 kHz) pulsations correlated well with the X-ray pulsations of the period corresponding to Pc 5. It is probable that the VLF- and ULF-associated X-rays or precipitating energetic electrons in the vicinity of the L ∼ 6 shell are in synchronization with the electron-cyclotron resonance. Lastly, the so-called ballooning-mirror instability (the BMI) is a candidate to explain the compressional MHD waves that occur during the short time interval (1216 MLT ∼ 1232 MLT) in which the experimental results were interpreted.

Solar‐wind‐driven pulsed magnetic reconnection at the dayside magnetopause, Pc5 compressional oscillations, and field line resonances

A series of observations by satellites of the solar wind and magnetosphere, by HF radars of the F region, and by ground‐based magnetometers of E region currents are presented to show the correlation between quasiperiodic fluctuations in the solar wind, magnetosphere, and ionosphere on January 24, 1996. The Iceland Stokkseyri SuperDARN radar observed quasiperiodic convection flow bursts in or near the ionospheric footprint of the cusp, identified by large spectral widths. Sometimes called flow channel events (FCEs), these enhanced convection flows are generally believed to be the ionospheric signatures of flux transfer events (FTEs) in the cusp. Initially, the flows pulsed with a periodicity of ∼12 min. When the “radar” cusp shifted to lower latitudes, possibly as a result of a series of FTEs, FCEs occurred every 10 min or less. The Wind spacecraft observed linearly polarized interplanetary magnetic field (IMF) oscillations with dominant periodicities of about 12 and 20 min (∼1.3 and 0.8 mHz) that were superposed on long‐period IMF fluctuations on the scale of a few hours. The pure state power spectra of the IMF components also showed several subsidiary peaks at higher frequencies (e.g., ∼1.7, 2.0, 2.4, and 2.9 mHz) or shorter periods (∼10, 8.5, 7, and 6 min). Similar oscillations were observed in the solar wind dynamic pressure which was anticorrelated with the IMF magnitude and included a strong oscillation with a period of ∼15 min (1.1 mHz). About 20 min later, in the postnoon magnetosheath, Geotail's magnetic and electric field sensors observed an ULF wave packet showing similar discrete spectra. The compressional MHD waves in the solar wind applied oscillating magnetic/electric fields and dynamic pressure on the dayside magnetopause driving multifrequency compressional oscillations in the magnetosphere. Discrete frequencies similar to those found in the solar wind and magnetosheath data were identified in the fast Fourier transform spectra of the ground‐based and space‐borne (GOES 8 and 9) magnetograms. A series of solar wind dynamic pressure pulses caused compressions and rarefactions of the magnetosphere observed by GOES 8 and GOES 9 magnetometers at geostationary orbit. The dynamic pressure driven magnetic perturbations, including those observed on the ground, propagated antisunward. In the noon sector the compressional waves coupled to shear modes resulting in propagation delays of the ground/ionospheric response. The convection flow bursts in the ionospheric footprint of the cusp were closely correlated with the low‐frequency oscillations of the IMF BZ and magnetosheath duskward electric field suggesting that the ULF waves in the solar wind modulated the magnetic reconnection at the dayside magnetopause into pulses. The higher‐frequency components of the IMF oscillations and/or sudden IMF changes excited field line resonances (FLRs) on the magnetic shells adjacent to the noon magnetopause. As the relative power of these higher‐frequency oscillations in the solar wind IMF increased and the cusp shifted to lower latitudes, the FCE rate also increased. A possibility of a reverse coupling (feedback) from the resonating magnetic shells to the reconnection region at the dayside magnetopause is suggested.

Transient response of the non-uniform equatorial ionosphere to compressional MHD waves

Abstract By assuming a realistic distribution of the height-integrated Cowling conductivity along the noon meridian, the transient response of the non-uniform equatorial ionosphere to plane compressional MHD waves is examined numerically. The direct incidence of an SC-type disturbance (or DL -field) on the ionosphere produces no preliminary reverse impulse (PRI) changes around the dayside equator, supporting the view that the equatorial PRI is caused by an extension of the ionospheric current responsible for the high-latitude PRI. The rise of the ground DL -field at the dip equator lags behind those in the off-equatorial region. This is a new finding which has not yet been reported observationally. When a magnetic pulsation is incident on the dayside ionosphere, the phase of the ground magnetic perturbation at the dip equator also lags behind those in the off-equatorial region. The phase lag at the dip equator obtained numerically agrees approximately with those observed for daytime Pi2 pulsations. However, the amplitude of the ground magnetic perturbation obtained numerically is depressed at the dip equator. Such a depression is contrary to the observational fact that the pulsation amplitude is enhanced at the dayside equator. Since there exists a sharp increase of the ionospheric zonal current at the dayside equator, the Pi2 pulsations around the dayside equator may also be due to the ionospheric current of polar origin.

On Jovian plasma sheet structure

We evaluate several models of Jovian plasma sheet structure by determining how well they organize several aspects of the observed Voyager 2 magnetic field characteristics as a function of Jovicentric radial distance. The present study focuses exclusively on the data from the Voyager 2 spacecraft because the magnetosphere was more stable during that flyby than it was during the Pioneer 10 and Voyager 1 flybys. It is shown that in the local time sector of the Voyager 2 outbound pass (near 0300 LT) the published hinged‐magnetodisc models with wave (i.e., models corrected for finite wave velocity effects) are more successful than the published magnetic anomaly model in predicting locations of current sheet crossings. We also consider the boundary between the plasma sheet and the magnetotail lobe which is expected to vary slowly with radial distance. We use this boundary location as a further test of the models of the magnetotail. The plasma‐sheet‐lobe boundary is often identified from the observed field gradients, the gradients in the lobes being much smaller than those in the plasma sheet. We show that the compressional MHD waves have much smaller amplitude in the lobes than in the plasma sheet and use this criterion to refine the identification of the plasma‐sheet‐lobe boundary. When the locations of crossings into and out of the lobes are examined, it becomes evident that the magnetic‐anomaly model yields a flaring plasma sheet with a halfwidth of ∼3 RJ at a radial distance of 20 RJ and ∼12 RJ at a radial distance of 100 RJ. The hinged‐magnetodisc models with wave, on the other hand, predict a halfwidth of ∼3.5 RJ independent of distance beyond 20 RJ. New optimized versions of the two models locate both the current sheet crossings and lobe encounters equally successfully. The optimized hinged‐magnetodisc model suggests that the wave velocity decreases with increasing radial distance. The optimized magnetic anomaly model yields lower velocity contrast than the model of Vasyliunas and Dessler (1981). The hinged‐magnetodisc models are shown to satisfy the constraints on the plasma sheet thickness imposed by MHD theory. The magnetic anomaly model can be made consistent with the expectations from MHD theory only by assuming plasma anisotropy so large that the plasma would be unstable to mirror mode instability. We recognize that the magnetic anomaly model is a comprehensive model designed to account for many features of the Jovian system as observed in multiple flyby missions. The plasma sheet structure for the Voyager 2 epoch is only one aspect of the model's predictions. Nonetheless, we believe that the model's failure to satisfy constraints on plasma sheet structure imposed by MHD equilibrium theory presents a challenge to the magnetic anomaly model as it is currently described.

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 B 0 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 B 0 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 B 0 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.

Quasi-periodical small-scale magnetic disturbances in the low-altitude cusp

Satellite data from measurements of thermal plasma and electric and magnetic fields are considered for the low-altitude cusp. Small-scale magnetic disturbances (SSMDs) are studied in relation to other plasma parameters. The SSMDs sometimes have a quasi-periodical structure and probably a compressional component. The analysis of their polarization structure provides grounds to conclude in some cases at least that the SSMDs represent compressional surface MHD waves.

Comment on the group velocity of surface waves on the plasma sheet boundary

In the recent estimation by Maltsev and Lyatsky (1984) of the group velocity of surface waves on the inner boundary of the plasma sheet, the effect of the curvature of the field lines of the ambient magnetic field of the Earth on the spectrum has been assessed. The authors have not accounted for the fact, however, that the group velocity of the compressional surface magnetohydrodynamic waves itself is nonzero transverse to the magnetic field—a characteristic which has been omitted in the spectrum of Chen and Hasegawa (1974), being used by Maltsev and Lyatsky. This characteristic of compressional surface MHD waves is inherent for the spectrum ω = ( k ‖ k )V A(k 2 ‖ + 2k 2 ⊥) 1 2 , obtained by Nenovski (1978) in the cold plasma limit V A ⪢ V S ( V A is Alfvén velocity, and V S , sound velocity). A comment has been made on the restrictions, proceeding from the approximation, used by Maltsev and Lyatsky. The estimation of the velocities for movements of auroral riometer absorption bays have been reviewed.