Coupled guided modes in the magnetotails: spatial structure and ballooning instability

The problem of the spatial structure of coupled azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved in an axisymmetric magnetotail model with a current sheet. It is shown that the linear transformation of these waves occurs in the current sheet on magnetic field lines stretched into the magnetotail. From the ionosphere to the current sheet these modes are linearly independent. Due to the high ionospheric conductivity the structure of coupled modes along magnetic field lines represents standing waves with very different typical scales in different parts of the field line. In most of the field line their structure is determined by the large-scale Alfvén wave structure. Near the ionosphere and in the current sheet, small-scale SMS wave field starts to dominate. In these regions coupled modes becomes small-scale. Such modes are neutrally stable on the field lines that do not cross the current sheet, but switch to the ballooning instability regime on field lines crossing the current sheet. An external source is required to generate these modes and this paper considers external currents in the ionosphere as a possible driver. In the direction across magnetic shells the coupled modes are waves running away from the magnetic shell on which they were generated.     

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.     

Modulational behavior of electromagnetic waves in ultra-relativistic electron-positron plasmas

The dynamical properties of electromagnetic (EM) waves in ultra-relativistic electron-positron (EP) plasmas are analytically investigated on the basis of the nonlinear governing equations obtained from a kinetic way. It is shown that the EM wave envelope will collapse and be trapped into a localized region for the modulation interaction with low frequency density variation induced by ponderomotive force. The correlation between the localized strong wave field and the pulsar radio emission is discussed.     

Strong cylindrical magnetogasdynamic shock waves in a rotating interplanetary medium

Strong cylindrical magnetogasdynamic shock waves in rotating interplanetary medium has been studied and an analytic solution for their propagation has been obtained. Using characteristic method and considering the effect of Coriolis force, we have shown that magnetic field has significant effect on the velocity of the shock wave.     

Magnetotail phenomena and auroral acceleration

It is suggested that localised electrostatic potential wells could be generated in the plasma sheet by large amplitude electrostatic ion cyclotron waves. It is shown from a consideration of a simple one dimensional model that such wells could possess a double structure of oppositely directed fields elongated in longitude. The possibility that the waves could evolve from a turbulent ion wave cascade driven by Earthward streaming protons is discussed and the magnitude of the potentials that could be established in this way is estimated using results for condensed state turbulent equilibria.The projections of these wells along the highly conducting geomagnetic field lines form potential valleys across the field lines in the high latitude auroral plasma. It is shown that these valleys would be of the scale and depth needed to establish electrostatic shocks which would be of sufficient intensity to accelerate electrons to energies comparable to those observed in “inverted-V” events. Potential wells are formed predominantly in the midnight sector of the plasma sheet and propagate Earthwards. This implies a corresponding equatorwards motion of the valley which, typically, would have a velocity of a few hundred m s^?1.     

MHD Modeling of Coronal Large-Amplitude Waves Related to CME Lift-off

We have employed a two-dimensional magnetohydrodynamic simulation code to study mass motions and large-amplitude coronal waves related to the lift-off of a coronal mass ejection (CME). The eruption of the filament is achieved by an artificial force acting on the plasma inside the flux rope. By varying the magnitude of this force, the reaction of the ambient corona to CMEs with different acceleration profiles can be studied. Our model of the ambient corona is gravitationally stratified with a quadrupolar magnetic field, resulting in an ambient Alfvén speed that increases as a function of height, as typically deduced for the low corona. The results of the simulations show that the erupting flux rope is surrounded by a shock front, which is strongest near the leading edge of the erupting mass, but also shows compression near the solar surface. For rapidly accelerating filaments, the shock front forms already in the low corona. Although the speed of the driver is less than the Alfvén speed near the top of the atmosphere, the shock survives in this region as well, but as a freely propagating wave. The leading edge of the shock becomes strong early enough to drive a metric type II burst in the corona. The speed of the weaker part of the shock front near the surface is lower, corresponding to the magnetosonic speed there. We analyze the (line-of-sight) emission measure of the corona during the simulation and recognize a wave receding from the eruption site, which strongly resembles EIT waves in the low corona. Behind the EIT wave, we clearly recognize a coronal dimming, also observed during CME lift-off. We point out that the morphology of the hot downstream region of the shock would be that of a hot erupting loop, so care has to be taken not to misinterpret soft X-ray imaging observations in this respect. Finally, the geometry of the magnetic field around the erupting mass is analyzed in terms of precipitation of particles accelerated in the eruption complex. Field lines connected to the shock are further away from the photospheric neutral line below the filament than the field lines connected to the current sheet below the flux rope. Thus, if the DC fields in the current sheet accelerate predominantly electrons and the shock accelerates ions, the geometry is consistent with recent observations of gamma rays being emitted further out from the neutral line than hard X-rays.     

Helicoidal magneto-electron waves in interstellar molecular clouds

We investigate the evolution of the magnetic flux density in a magnetically supported molecular cloud driven by Hall and Ohmic components of the electric field generated by the flows of thermal electrons. Particular attention is given to the wave transport of the magnetic field in a cloud whose gas dynamics is dominated by electron flows; the mobility of neutrals and ions is regarded as heavily suppressed. It is shown that electromagnetic waves penetrating such a cloud can be converted into helicons – weakly damped, circularly polarized waves in which the densities of the magnetic flux and the electron current undergo coherent oscillations. These waves are interesting in their own right, because for electron magnetohydrodynamics the low-frequency helicoidal waves have the same physical significance as the transverse Alfvén waves do for a single-component magnetohydrodynamics. The latter, as is known, are considered to be responsible for the widths of molecular lines detected in dark, magnetically supported clouds. From our numerical estimates for the group velocity and the rate of dissipation of helicons it follows that a possible contribution of these waves to the broadening of molecular lines is consistent with the conditions typical of dark molecular clouds.     

On the resonant modes of a cavity and the dynamical properties of micropulsations

Certain classes of micropulsations are customarily explained in terms of guided (toroidal) and isotropic (poloidal) hydromagnetic waves m the magnetosphere. The physical properties of these waves are not well understood and their utility in explaining observed polarization patterns is questionable. In an effort to understand and explain the physics underlying these modes, a study is made of a cylindrical cavity (the hydromagnetic wedge), filled with a plasma having a large but finite conductivity and magnetized by an azimuthal magnetic field. Coupling between the toroidal and poloidal modes is effected by the inclusion of the Hall current in the generalized Ohm's law. Physically meaningful solutions to the wave equation are obtained and the toroidal eigenfunctions are demonstrated to be non-degenerate and well-behaved throughout the configuration, and exhibit for each mode a unique spatial resonance whose location, given by a line of force, is specified by the corresponding eigenvalue. The non-degenerate, discrete and spatially independent eigenvalues for the modes are shown to obey a selection rule that limits the spectrum. For a given mode, the states of polarization of the transverse field are determined and it is shown (as has been observed) that, depending on the line of force singled out, the magnetic polarization may be linear, elliptical or circular, right or left-handed, and whatever the state, it is immutable along the line of force. More complicated polarization patterns are derived and explained by superposing different modes vectorially. Classical concepts such as guided and isotropic modes and vibrating field lines are reinterpreted and evaluated in terms of the model. To examine the dependence of modal amplitude on source, the amplitude is expressed in terms of a sinusoidal driving pressure for a simple steady-state case. Symmetries of the model and the magnetosphere are specified and the detailed numerical results are ‘scaled’ for plasmaspheric application. The resonant spectrum, encompassing pc 2–4, is described and the variation of period spectrum with magnetic latitude and activity is presented. The agreement between the semi-quantitative analysis and the observational results is sufficiently close to indicate that the basic physics of the model encompasses the fundamental dynamics of pc activity.     

The mechanism of magnetospheric substorm and the MHD waves of the solar wind

A mechanism of the Earth's magnetospheric substorm is proposed. It is suggested that the MHD waves may propagate across the magnetopause from the magnetosheath into the magnetotail and will be dissipated in the plasma sheet, heating the plasma and accelerating the particles. When the solar wind parameters change, the Poynting flux of the waves transferred from the magnetosheath into the tail, may be greater than 10¹⁸ erg s^?1. The heated plasma and accelerated particles in the plasma sheet will be injected into the inner magnetosphere, and this may explain the process of the ring current formation and auroral substorm.The Alfvén wave can only propagate along the magnetic force line into the magnetosphere in the open magnetosphere, but the magnetosonic wave can propagate in both the open and closed magnetosphere. When the IMF turns southward, the configuration of the magnetosphere will change from a nearly closed model into some kind of open one. The energy flux of Alfvén waves is generally larger than that of the magnetosonic wave. This implies that it is easy to produce substorms when the interplanetary magnetic field (IMF) has a large southward component, but the substorm can also be produced even if the IMF is directed northward.     

The umbral flash as a magneto-acoustic wave phenomenon

The suggestion that an umbra flash may be caused by a magneto-acoustic wave phenomenon is examined. It is suggested that the flash in Ca ii lines is formed during the compressional stage in a magneto-acoustic wave. The compression which is assumed to be adiabatic will produce a rise in temperature and a corresponding increase in number of Ca ii atoms. The variations in line emission (absorption) coefficient of the Ca ii K-line are calculated on this assumption and are found to be in general agreement with the observed variations. Other observed quantities as proper motion, magnitude of line shift etc., also agree with the wave hypothesis. Further observations which may serve as tests on the wave hypothesis are suggested.     

Whistler mode propagation through weakly ionized magnetoplasma

The VLF wave generation by ?erenkov process from weakly ionized plasma has been considered. The effect of collisions on ?erenkov power spectrum and on propagation of VLF waves in whistler mode has been studied. The radiated power is shown to depend on the collisional parameter. The presence of collisions is found to modify the refractive index surfaces. It is shown that the focussing of VLF waves is less probable in the presence of collisions.     

Frequency shift of space-charge waves in a relativistic electron or positron beam

Nonlinear frequency shift of space-charge waves in a relativistic electron or positron beam is analyzed. The frequency shift is shown to be a function of the wave amplitude. It is suggested that the frequency shift of beam space-charge waves may be a saturation mechanism for astrophysical free-electron lasers.     

An explosion with cylindrical symmetry in magnetogasdynamics

The propagation of magnetogasdynamic cylindrical shock waves in an exponentially increasing medium including the effects of the azimuthal magnetic field, is investigated. The shock wave moves with variable velocity and the total energy of the wave is variable. It is shown that the magnetic field has its significant effect on the pressure flow velocity and the inner expanding vacuum region.     

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.     

Hydromagnetic-gravity wave critical levels in the solar atmosphere

It is shown that the discontinuous jump in the vertical wave energy flux of slow hydromagnetic-gravity waves, occurring at a critical level, which is accompanied by wave absorption, and the existence of a reflection point imply that slow waves are trapped in the solar atmosphere. Thus such a system behaves as a leaky wave guide.     

星系盘厚度效应的研究

在三维引力Poisson方程严格解基础上，探讨了有限厚星系盘基盘的动力学性质，并进一步讨论了盘的厚度效应对银河系所需晕质量的影响。研究了扰动盘的动力学性质，通过将扰动引力势Poisson方程的严格解与林家翘、徐遐生提出的自维持密度波理论相结合，建立了三维旋涡星系有限厚盘上密度波的色散关系。在此色散关系的基础上讨论了盘的局域稳定性，研究了旋涡星系旋臂的形态、三维盘状星系密度波的群速度。研究表明厚度是星系盘研究中不容忽略的重要参量。另外在有限厚盘星系密度波色散关系的基础上还探讨了一种确定星系厚度的新方法。     

Stokes Diagnostics of Magneto-Acoustic Wave Propagation in the Magnetic Network on the Sun

The solar atmosphere is magnetically structured and highly dynamic. Owing to the dynamic nature of the regions in which the magnetic structures exist, waves can be excited in them. Numerical investigations of wave propagation in small-scale magnetic flux concentrations in the magnetic network on the Sun have shown that the nature of the excited modes depends on the value of plasma β (the ratio of gas to magnetic pressure) where the driving motion occurs. Considering that these waves should give rise to observable characteristic signatures, we have attempted a study of synthesised emergent spectra from numerical simulations of magneto-acoustic wave propagation. We find that the signatures of wave propagation in a magnetic element can be detected when the spatial resolution is sufficiently high to clearly resolve it, enabling observations in different regions within the flux concentration. The possibility to probe various lines of sight around the flux concentration bears the potential to reveal different modes of the magnetohydrodynamic waves and mode conversion. We highlight the feasibility of using the Stokes-V asymmetries as a diagnostic tool to study the wave propagation within magnetic flux concentrations. These quantities can possibly be compared with existing and new observations in order to place constraints on different wave excitation mechanisms.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.