The sideband instability of electrostatic waves in an inhomogeneous medium

The work deals with the resonant particle excitation of two electrostatic waves with closely spaced wave numbers, when there is an inhomogeneity present in the form of a spatially dependent wave number. Resonant particle behaviour in such a field is investigated and the resonant particle current is computed for a variety of cases. If the inhomogeneity is such that resonant particles see the wave numbers of the waves increasing, then it turns out that the wave of greatest wave number is preferentially amplified. If the gradient is reversed it is the opposite wave which grows. Thus when a narrow band electrostatic wave is subject to beam excitation, only one of the sideband waves is unstable.The theory is applied to the closely analogous problem of sideband formation in the case of triggering of VLF emissions by magnetospheric whistler pulses, and seems to account for much of the observed behaviour.     

Hydromagnetic waves as a cause of a SAR arc event

A study is made of the hydromagnetic wave activity observed on the ground during the sub-auroral red (SAR) arc event of 17–18 December 1971. The available wave energy flux in the magnetosphere, inferred from the observed wave amplitude on the ground using the present understandings of wave localization and ionosphere wave attenuation is sufficient to produce the SAR arc. This finding supports kinetic Alfvén wave heating as a production mechanism for SAR arc optical emissions.     

Hydromagnetic field line resonances and modulation of particle precipitation

Hydromagnetic wave and modulated particle precipitation data are reported from conjugate areas near the particledrift shell L ～ 4. A modulation of electrons precipitating from the magnetosphere is observed in the conjugate regions when the accompanying hydromagnetic wave period is ~ 90 s and the wave polarization is linear. When the wave period changes abruptly to ~ 30 s and the polarizations at the observing stations are no longer linear, the modulation of the precipitating electrons is no longer observed. The change in hydromagnetic wave characteristics does not appear to be related to interplanetary plasma and magnetic field conditions. Rather, it is proposed to arise from a change in the wave generation mechanism from an internal magnetospheric source near the inner edge of the plasmapause (lower frequency) to an externally driven source outside the magnetosphere (higher frequency). This observation of a change in the wave characteristics (frequency and polarization) associated with modulated electron precipitation appears to be related to two previous examples wherein modulated electron precipitation was reported to be closely associated with the existence of a wave resonance region near the observing site.     

Whistler wave generation by parametric decay of fast ion-acoustic waves

It is shown that a fast ion-acoustic wave can decay into another ion-acoustic wave and a whistler wave. The results are applied to interpret wave spectra measurements in the foreshock region of the Earth's bowshock.     

Formation of Coronal Shock Waves

Magnetosonic wave formation driven by an expanding cylindrical piston is numerically simulated to obtain better physical insight into the initiation and evolution of large-scale coronal waves caused by coronal eruptions. Several very basic initial configurations are employed to analyze intrinsic characteristics of MHD wave formation that do not depend on specific properties of the environment. It turns out that these simple initial configurations result in piston/wave morphologies and kinematics that reproduce common characteristics of coronal waves. In the initial stage, the wave and the expanding source region cannot be clearly resolved; i.e. a certain time is needed before the wave detaches from the piston. Thereafter, it continues to travel as what is called a “simple wave.” During the acceleration stage of the source region inflation, the wave is driven by the piston expansion, so its amplitude and phase-speed increase, whereas the wavefront profile steepens. At a given point, a discontinuity forms in the wavefront profile; i.e. the leading edge of the wave becomes shocked. The time/distance required for the shock formation is shorter for a more impulsive source-region expansion. After the piston stops, the wave amplitude and phase speed start to decrease. During the expansion, most of the source region becomes strongly rarefied, which reproduces the coronal dimming left behind the eruption. However, the density increases at the source-region boundary, and stays enhanced even after the expansion stops, which might explain stationary brightenings that are sometimes observed at the edges of the erupted coronal structure. Also, in the rear of the wave a weak density depletion develops, trailing the wave, which is sometimes observed as weak transient coronal dimming. Finally, we find a well-defined relationship between the impulsiveness of the source-region expansion and the wave amplitude and phase speed. The results for the cylindrical piston are also compared with the outcome for a planar wave that is formed by a one-dimensional piston, to find out how different geometries affect the evolution of the wave.     

Alfvén turbulence in collisionless plasmas

The evolution of Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. In particular, we consider decay of Alfvén waves through three-wave coupling with an ion sound mode in the random-phase approximation. Two decay processes are of particular interest: an Alfvén wave decays into a backward propagating Alfvén wave and a forward propagating ion sound wave, and an Alfvén wave decays into a backward propagating fast magnetoacoustic wave and a forward ion sound wave. The former was widely discussed in the literature, particularly under the coherent wave assumption. The latter was not well explored and is discussed here.     

Propagation of auroral infrasonic waves studied by ray-tracings

On the basis of a ray tracing method the propagation and the attenuation of an auroral infrasonic wave are studied. Relations between the direct and reflected waves recorded at the Syowa Station, Antarctica, are clarified with regard to; (1) the delay time, (2) the intensity ratio, and (3) trace velocities. The time required for a wave to travel from the source to the ground is calculated as a function of a source altitude. The retardation time of the wave arrival behind the zenith crossing of the source current is deduced. A method is proposed for estimating the altitude of a source current from the retardation and a trace velocity of the wave. It is concluded that the existence of a supersonic equatorward motion of an electrojet which continues for a certain distance is necessary for the observation of auroral infrasonic waves. This distance must exceed at least 60 km equatorwards from the zenith to enable the direct wave to be observed and with total length of 930 km to enable the reflected wave to be observed. From these conditions it is also concluded that the infrasonic wave is not seen in mid latitudes and the reflected wave is a rare phenomenon.     

Reverse shock wave in relativistic explosions

The dynamical evolution of a relativistic explosion in a homogeneous medium is studied by means of a time-dependent, hydrodynamic code. When the expanding velocity of the shock front reduces to the sound velocity in the relativistic fluid, the reverse shock wave propagating inward through the expanding material is generated. The radius of the turning point of the reverse shock wave is proportional to the explosion energy and hardly depends on the mass of the explosion products. In the case of the non-relativistic explosion, the reverse shock wave is generated just after the free expansion stage. The radius of the turning point of the reverse shock wave is proportional to the mass of the explosion products and little depends on the explosion energy. In both cases of the non-relativistic and relativistic explosion, the reverse shock wave is strong in a spherical explosion and weak in a cylindrical one. The plane symmetric explosion does not generate the reverse shock wave.     

The coupling resonance of torsional alfven wave and fast wave in coronal loops

The method of Orthogonal Function Series Expansion (OFSE) is generalized and applied to the study of the evolution of the coupling of nondissipative torsional Alfven wave and fast wave in coronal loops. Using this method, the intrinsic angular frequency of the overall wave mode can be described mathematically and that of the Alfven waves along the magnetic lines in the coronal loop during the coupling of the Alfven and fast waves can be analyzed both theoretically and numerically. Also with this method, the relation between the coupling driven term and the Alfven wave resonance may be analyzed. Results of computation reveal the place of appearance of coupling resonance as well as the characteristics of the amplitudes of the Alfven and fast waves. As found by the calculations, if the footpoint driven angular frequency is not equal to the intrinsic angular frequency of the overall wave mode of the coronal loop and when a δ section appears at the place of coupled resonance, the radial gradient of the fast wave's amplitude is quite large. Sometimes it approximates to a discontinuity, and this is extremely favorable for the dissipation of the fast wave. If the footpoint driven angular frequency is equal to the intrinsic angular frequency of the overall wave mode and when a δ section occurs in the Alfven wave amplitude, abundant small-scale structures appear in the radial direction. Then the location of resonance approximately becomes a discontinuity, very favorable to the dissipation of the Alfven wave.     

Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics

We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel–Kramers–Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.     

VLF two-wave-electron interactions in the magnetosphere

The mutual influence between two whistler mode waves, through cyclotron resonant interaction of each wave with the same set of energetic electrons, is analysed both theoretically and by computer simulations ; this two-wave interaction mechanism seems to be an important process in understanding recently observed phenomena in Siple Station VLF multi-wave injection experiments. A criterion is established to estimate the threshold for the critical frequency spacing (for given wave amplitudes) for a significant mutual interaction between two monochromatic waves to occur. This criterion is based on the overlap of coherence bandwidths associated with the trapping domains of each wave and it takes into account the geomagnetospheric medium inhomogeneity. The effects of a perturbing second wave on electrons trapped by a first wave is discussed, considering the general situation of varying-frequency waves, and a simulation model is used to track the motion of test-electrons in the two-waves field. Conditions leading to detrapping and subsequent trapping by the second wave of previously first-wave trapped electrons are analysed and suggest the possibility of this phenomenon to play an important role in frequency entrainment and energy exchange between two waves.     

Coupling equations for a flow-wave field used to faculae heating

In a binary system of a background fluid-wave field, the wave effect may be important in some cases. From general properties of thermodynamics of the medium, we derive the coupling equations for the mean flow-wave field. For six wave modes (Langmuir wave, ion-acoustic oscillations, whistlers, Alfvén waves, magneto-acoustic oscillations, and transverse plasma wave) the corresponding representation of the wave stress tensor is found. Finally, the representation for the Alfvén waves is applied to the faculae heating and a result consistent with observations is obtained.     

Viscous damping of surface magnetohydrodynamic waves on magnetic interface in cold plasmas

Surface magnetohydrodynamic wave propagation on a magnetic interface in a cold plasma is studied. The anisotropic ion viscosity is taken into account. Only long waves damping weakly in a wave period are considered. The dispersion equation is obtained. This equation is shown always to have exactly one root if there is no viscosity. The dependences of phase velocity, penetration depth and damping decrement of waves on the parameters of undisturbed plasma and wave propagation direction are investigated. The resulting application for describing of surface wave damping in the solar corona is discussed.     

Nonlinear shift of wave parameters of whistlers in the ionosphere

The expression for nonlinear shift of a wave number of a whistler wave propagating through the ionosphere has been derived and the results have been discussed. It is seen that nonlinear shift of a wave number of a whistler is significant in some physical situations. From numerical estimations it is observed that wave number shifts of a whistler for both the LCP and RCP waves become significant when the frequency of the waves are nearly equal to the ion-cyclotron frequency.     

Guided waves in magnetospheric tubes of enhanced density

Properties of a guided MHD-wave propagating in a magnetic field tube with the plasma density differing from the ambient density are studied. Like the Alvén wave this wave propagates along the magnetic field and is connected with the field-aligned currents flowing at the periphery of the oscillating tube. The guided wave is accompanied by the magnetic field compression, nevertheless the wave moves without attenuation. The guided wave velocity is between the Alvén velocities inside and outside the oscillating tube. In a tube of elliptical cross-section the propagation velocity depends on the polarization of the wave.     

Phase-bunching and other non-linear processes occurring in gyroresonant wave-particle interactions

We consider the movement of individual electrons in a magnetized plasma in which a monochromatic wave is propagating in the whistler mode. We derive simple expressions which give the displacement of the electrons as a function of time, the phase angle that their velocity vector makes with the magnetic component of the wave, their pitch angle and energy changes. A useful formula is obtained which gives the velocity range over which particles remain trapped inside the wave, as a function of the wave intensity and of the initial phase angle of the particle. It is shown that even strictly resonant particles can escape from the wave when their initial phase angle is very small. From the derived expressions, it is possible to compute the phase-bunching effect which occurs approximately at one trapping wavelength behind the leading edge of the interaction region. We deduce also the total amount of energy which is taken from (or given to) the wave by magnetospheric electrons in both cases of naturally existing or artificially injected particles. It is shown that these non-linear amplification processes can lead to very large VLF amplitude in the magnetosphere.     

Trapping of electromagnetic waves by nonlinear resonant interactions with ion sound waves

Resonant wave-wave interaction among one ion sound wave and two electro-magnetic waves in an isotropic plasma is studied. The emphasis is on the possibility of trapping the electromagnetic wave. Equations for the three-wave system are derived. One particularly interesting case is that for which the frequency of ion sound wave is much less than the frequency of electromagnetic waves. For this case it is shown that energy exchange takes place only between the two high frequency waves. The ion sound wave does not participate in the energy exchange process but acts as a kind of catalyst for the interaction. Simple solutions are obtained. It is found that the electromagnetic energy is trapped within a certain spatial region. The trapping width is found to depend, among other parameters, on the magnitude of ion sound wave perturbation. Possible application of the theory to topside ionospheric observations of field-aligned propagation is discussed.     

Perturbations of a twisted solar coronal loop: The relation between surface waves and instabilities

The spectrum of propagating waves and instabilities on a current-carrying, zero gas pressure, twisted magnetic flux loop is analysed for several models of the magnetic field structure. A surface wave mode of the fast Alfvén wave is found to exist, with damping of the wave when Alfvén resonance absorption occurs. If the loop is surrounded by a uniform, purely axial magnetic field, then the surface wave is always stable. If the loop is surrounded by a nonuniform field which is continuous with the loop's field, then the surface wave may connect to the unstable external kink mode.     

引力波和引力波望远镜的发展

简要回顾了广义相对论中相关的引力波理论，讨论了对引力波进行探测的重要意义和几种可能的途径；系统介绍了近50年来国际上对引力波进行探测的主要活动，以及当前几个具有代表性的引力波望远镜工程的进展。     

Magneto-atmospheric waves from a localized source

A technique developed by Lighthill for finding the asymptotic solution of an inhomogeneous wave equation with constant coefficients is applied to the study of wave propagation in magneto-atmospheres. The geometry of the wave number surface plays an important role in determining the generation and propagation of various types of magneto-atmospheric waves from a localized forcing region. Examples of these wavenumber surfaces are exhibited for various magnetic field strengths and wave frequencies. The asymptotic far field is tabulated for a time-harmonic, spatially gaussian, localized forcing term.