High-frequency waves in hot magnetized solar and stellar coronal plasmas

The characteristics of low-damping high-frequency waves in hot magnetized solar and stellar coronal plasmas under the conditions when the electron gyrofrequency ω_He is equal to or higher than the electron plasma frequency ω_pe have been analyzed using the numerical solution of the dispersion equation. It is shown that the wave branches corresponding to the Z mode and ordinary waves approach each other when the magnetic field increases and become almost indistinguishable in a wide frequency range at all angles between the wave vector and magnetic field. A branch with anomalous dispersion appears at angles close to 90°. A new interpretation of broadband pulsations and spikes is suggested on the basis of the results.     

Low frequency waves in plasmas with spatially varying electron temperature

Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B₀ and low frequency waves (_ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (_ci) will on the other hand have a spatially more uniform intensity distribution.     

WIND observations of coherent electrostatic waves in the solar wind

The time domain sampler (TDS) experiment on WIND measures electric and magnetic wave forms with a sampling rate which reaches 120 000 points per second. We analyse here observations made in the solar wind near the Lagrange point L1. In the range of frequencies above the proton plasma frequency f_pi and smaller than or of the order of the electron plasma frequency f_pe, TDS observed three kinds of electrostatic (e.s.) waves: coherent wave packets of Langmuir waves with frequencies f ≃ f_pe, coherent wave packets with frequencies in the ion acoustic range f_pi ≥ f ≥ f_pe, and more or less isolated non-sinusoidal spikes lasting less than 1 ms. We confirm that the observed frequency of the low frequency (LF) ion acoustic wave packets is dominated by the Doppler effect: the wavelengths are short, 10 to 50 electron Debye lengths λ_D. The electric field in the isolated electrostatic structures (IES) and in the LF wave packets is more or less aligned with the solar wind magnetic field. Across the IES, which have a spatial width of the order of ≃25_D, there is a small but finite electric potential drop, implying an average electric field generally directed away from the Sun. The IES wave forms, which have not been previously reported in the solar wind, are similar, although with a smaller amplitude, to the weak double layers observed in the auroral regions, and to the electrostatic solitary waves observed in other regions in the magnetosphere. We have also studied the solar wind conditions which favour the occurrence of the three kinds of waves: all these e.s. waves are observed more or less continuously in the whole solar wind (except in the densest regions where a parasite prevents the TDS observations). The type (wave packet or IES) of the observed LF waves is mainly determined by the proton temperature and by the direction of the magnetic field, which themselves depend on the latitude of WIND with respect to the heliospheric current sheet.     

Determination of the dispersion of low frequency waves downstream of a quasiperpendicular collisionless shock

A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves V_int = V_acos().     

Compressional wave events in the dawn plasma sheet observed by Interball-1

Compressional waves with periods greater than 2 min (about 10–30 min) at low geomagnetic latitudes, namely compressional Pc5 waves, are studied. The data set obtained with magnetometer MIF-M and plasma analyzer instrument CORALL on board the Interball-1 are analyzed. Measurements performed in October 1995 and October 1996 in the dawn plasma sheet at −30 R_E ≤ X_GSM and |Z_GSM| ≤ 10 R_E are considered. Anti-phase variations of magnetic field and ion plasma pressures are analyzed by searching for morphological similarities in the two time series. It is found that longitudinal and transverse magnetic field variations with respect to the background magnetic field are of the same order of magnitude. Plasma velocities are processed for each time period of the local dissimilarity in the pressure time series. VeloCity disturbances occur mainly transversely to the local field line. The data reveal the rotation of the veloCity vector. Because of the field line curvature, there is no fixed position of the rotational plane in the space. These vortices are localized in the regions of anti-phase variations of the magnetic field and plasma pressures, and the vortical flows are associated with the compressional Pc5 wave process. A theoretical model is proposed to explain the main features of the nonlinear wave processes. Our main goal is to study coupling of drift Alfven wave and magnetosonic wave in a warm inhomogeneous plasma. A vortex is the partial solution of the set of the equations when the compression is neglected. A compression effect gives rise to a nonlinear soliton-like solution.     

Nonlinear plasma wave processes observed in the polar cusp

We present observations of electric and magnetic field variations from proton (about few Hz) to electron cyclotron frequencies (about few kHz) obtained by STAFF instrument on Cluster satellites during two cusp crossings, at ∼6 R _E altitude, in September 2002. The cusp was identified by the presence of intensive fluxes of counter streaming electrons with low energies and broadband wave activity which is typical for this region. Special attention is given for the interval of measurements when the waveform of the magnetic field fluctuations was taken in this region by CLUSTER satellites. The wave has been processed using the wavelet and bispectral analysis. Results showing the cascade of turbulence and wave-wave interactions are presented in this paper. A three wave process can be responsible for the broadening of the wave spectra in the polar cusp.     

Geophysical phenomena during an ionospheric modification experiment at Tromsø, Norway

We present an analysis of phenomena observed by HF distance-diagnostic tools located in St. Petersburg combined with multi-instrument observation at Tromsø in the HF modified ionosphere during a magnetospheric substorm. The observed phenomena that occurred during the Tromsø heating experiment in the nightside auroral E_s region of the ionosphere depend on the phase of substorm. The heating excited small-scale field-aligned irregularities in the E region responsible for field-aligned scattering of diagnostic HF waves. The equipment used in the experiment was sensitive to electron density irregularities with wavelengths 12–15 m across the geomagnetic field lines. Analysis of the Doppler measurement data shows the appearance of quasiperiodic variations with a Doppler frequency shift, f_d and periods about 100–120 s during the heating cycle coinciding in time with the first substorm activation and initiation of the upward field-aligned currents. A relationship between wave variations in f_d and magnetic pulsations in the Y-component of the geomagnetic field at Tromsø was detected. The analysis of the magnetic field variations from the IMAGE magnetometer stations shows that ULF waves occurred, not only at Tromsø, but in the adjacent area bounded by geographical latitudes from 70.5° to 68° and longitudes from 16° to 27°. It is suggested that the ULF observed can result from superposition of the natural and heater-induced ULF waves. During the substorm expansion a strong stimulated electromagnetic emission (SEE) at the third harmonic of the downshifted maximum frequency was found. It is believed that SEE is accompanied by excitation of the VLF waves penetrating into magneto-sphere and stimulating the precipitation of the energetic electrons (10–40 keV) of about 1-min duration. This is due to a cyclotron resonant interaction of natural precipitating electrons (1–10 keV) with heater-induced whistler waves in the magnetosphere. It is reasonable to suppose that a new substorm activation, exactly above Tromsø, was closely connected with the heater-induced precipitation of energetic electrons.     

Investigation of the broadband ELF turbulence by observations of the FAST satellite

Scaling properties of variable electric fields in the topside ionosphere have been investigated on scales s from ∼30 m to 2 km by FAST electric field observations with sample rate of 512 s⁻¹, in sixteen events of the broadband ELF turbulence. It is shown that down to scales of a few hundred meters, the power of turbulent electric fluctuations is a power law, ∼s ^α. Scaling index α derived from the slope of logarithmic diagrams (LD) constructed by the discrete wavelet transform of data can be estimated as α = 2.2 ± 0.3, which is close to α estimate earlier reported for scales 1–30 km by electric field observations of the Dynamics Explorer 2 satellite. The behavior of α index is analyzed near the scale of the order of electron inertial length λ_e = c/ω₀ (ω₀ being the electron plasma frequency). At altitudes considered (700–2500 km), λ_e makes 100–900 m. We demonstrate that at scales ≤λ_e, a decrease of LD slope and deviation from the power law are typically observed. As pointed out in the discussion, this feature cannot be identified as a transition to the diffusion range, where dissipation of the turbulence occurs.     

Q P and Q S in Beijing and Jianchuan, Yunnan areas

Events from the December 1982 Huairou County, Beijing, and the July 1982 Jianchuan, Yunnan earthquake series were recorded at one station in Beijing City and at four stations in Eryuan area, Yunnan, respectively. Dividing the spectra (for P and S waves) from the smaller events in the series by spectra (for corresponding P and S waves) from the larger events in cach region, we have determined the high frequency source spectral decay rate to be ω⁻¹in both cases. Through trial and error method, we are able to determine the appropriate constantQ _P andQ _S that corrects the individual spectra to the proper high frequency decay rate. It is found that aQ _P of 800 and aQ _S of 550 can adequately compensate for the attenuation of the waves in Beijing area. For Jianchuan, Yunnan area the corresponding values are 900 and 400. This subject is supported by Chinese Joint Seismological Science Foundation.     

Pc1 pearl waves with magnetosonic dispersion

Results of the analysis of 15 unusual Pc1 pearl wave events with inverse dispersion in comparison with the dispersion of well-known electromagnetic ion-cyclotron (EMIC) waves in the form of classic pearl pulsations are presented. Pulsations with the dynamical spectrum consisting of both falling tones only (first type) and events with structures, which start with the falling tones and then develop into rising tones (second type), have been discovered. The first type corresponds to the frequency dispersion of magnetosonic waves (R-waves), and the second type corresponds to the mixed frequency dispersion of R-waves and EMIC waves (L-waves). All events were observed during quiet geomagnetic periods. The duration of the events is about 20–30 min. For the interpretation of these phenomena, the cyclotron instability driven by energetic proton beams with relative mean velocity v₀ directed along the background magnetic field and corresponding to an energy ∼10–100 keV is considered. The interaction of such proton beams with waves having frequencies ω<ω_i (ω_i is the ion gyrofrequency) leads to the instability, which allows the fastest growth of electromagnetic oscillations with the dispersion of R-wave type. When the velocity of the proton beam decreases (v₀≈0), R-waves attenuate and L-waves (for the proton temperature T_⊥>T_∥) will be amplified. This instability is the reason for the generation of classic Pc1 pearl pulsations with the usual dispersion and allows explaining the transition of the dispersion from R- to L-waves.     

Propagation of magneto-elastic waves in a perfectly conducting plate extending to infinity in vacuum

Summary The effects of a uniform external magnetic field on the propagation of waves in a homogeneous, infinitely conducting flat plate with free boundaries have been studied. It has been found that in general all the three types of waves —P, SV andSH waves—are coupled and the influence may be more pronounced in coupling the symmetric and antisymmetric types of motions in every mode.When the magnetic field is parallel to the plane faces and transverse to the direction of wave propagation, the shear wave polarized parallel to the field is purely elastic whereas the coupledP andS V waves are magnetoelastic and exhibit dispersion strikingly similar to the non-magnetic case, provided the electro-magnetic radiation into the surrounding free space is neglected.The results reported in an earlier communication [1]²) are also confirmed.     

Wave activity in the ionosphere during the geospace storm of November 7–10, 2004

This paper presents the results of studies of wave disturbances in the electron concentration N in the ionosphere during a prominent geospace storm, in the process of which the electron concentration decreased by a factor of 6–7, whereas the temperatures of ions and electrons at night increased up to 2000 and 3000 K, respectively. The height-time variations in the parameters of wave disturbances are also analyzed. It is shown that the geospace storm was accompanied by a substantial change in wave activity in the ionosphere. In the period of negative ionospheric storms, the amplitude Δ _N decreased by a factor of 2–10. At the same time, the relative amplitude δ _N = ΔN/N changed insignificantly and was within the limits 0.05–0.10 during day-time. At night, δ _N reached 0.25–0.30 and sometimes even 0.4–0.5. During both disturbed and undisturbed days, quasi-periodic processes with a period of 40–60 and 80–120 min prevailed. The maximum values of the absolute and relative amplitudes were achieved at a height of 200–270 km. A soliton-like disturbance formed near the main phase of the magnetic storm on November 10, 2004 was detected. Its appearance was related to the oblique coherent reflection of sounding signals.     

Estimation of the quality factor in shallow soil using surface waves

IntroductionVelocityanditsattenuationinformationiscloselylinkedwiththeoreticalstudiesonthegroundmovementsduringearthquake.Therecentstudy(Malagnini,1996)showedthatthevelocitystructureofshearwaveinshallowsoilabove30mplaysanimpoftantroletoestimatestfonggroundmotionofsite.However,itishardtopreciselymeasurethesoilstructuresanddynamiccharacteristics.First,theloosesoilabsorbstheseismicwaveswithhighfrequencies;Second,theeffectsoffocusinganddispersioncausedbylocallyinhomogeneoussitecannotbeneglectedin…     

Wave propagation in a seven-story reinforced concrete building: I. Theoretical models

For transient, high frequency, and pulse like excitation of structures in the near field of strong earthquakes, the classical design approach based on relative response spectrum and mode superposition may not be conservative. For such excitations, it is more natural to use wave propagation methods. In this paper (Part I), we review several two-dimensional wave propagation models of buildings and show results for theoretical dispersion curves computed for these models. We also estimate the parameters of these models that would correspond to a seven-story reinforced concrete building in Van Nuys, California. Ambient vibration tests data for this building imply vertical shear wave velocity β_z=112 m/s and anisotropy factor β_x/β_z=0.55 for NS vibrations, and β_z=88 m/s and β_x/β_z=1 for EW vibrations. The velocity of shear waves propagating through the slabs is estimated to be about 2000 m/s. In the companion paper (Part II), we estimate phase velocities of vertically and horizontally propagating waves between seven pairs of recording points in the building using recorded response to four earthquakes.     

Energy mode distribution: An analysis of the ratio of anti-Stokes to Stokes amplitudes generated by a pair of counterpropagating Langmuir waves

Results from plasma wave experiments in spacecrafts give support to nonlinear interactions involving Langmuir, electromagnetic, and ion-acoustic waves in association with type III solar radio bursts. Starting from a general form of Zakharov equation (Zakharov, V.E., 1985. Collapse and self-focusing of Langmuir waves. Hand-book of Plasma Physics Cap.2, 81–121) the equations for electric fields and density fluctuations (density gratings) induced by a pair of counterpropagating Langmuir waves are obtained. We consider the coupling of four triplets. Each two triplets have in common the Langmuir pump wave (forward or backward wave) and a pair of independent density gratings. We numerically solve the dispersion relation for the system, extending the work of (Alves, M.V., Chian, A.C.L., Moraes, M.A.E., Abalde, J.R., Rizzato, F.B., 2002. A theory of the fundamental plasma emission of type- III solar radio bursts. Astronomy and Astrophysics 390, 351–357). The ratio of anti-Stokes (AS) (ω₀+ω) to Stokes (S) (ω₀-ω^*) electromagnetic mode amplitudes is obtained as a function of the pump wave frequency, wave number, and energy. We notice that the simultaneous excitation of AS and S distinguishable modes, i.e., with Re{ω}=ω_r≠0, only occurs when the ratio between the pump wave amplitudes, r is ≠1 and the pump wave vector k₀ is , W₀ being the forward pump wave energy. We also observe that the S mode always receives more energy.     

Lateral variations of coda Q and attenuation of seismic waves in Southwest Anatolia

The seismic quality factor (Q _c) and the attenuation coefficient (δ) in the earth’s crust in southwest (SW) Anatolia are estimated by using the coda wave method based on the decrease of coda wave amplitude by time on the seismogram. The quality factor Q _o, the value of Q _c at 1 Hz, and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves. δ is determined from the observations of amplitude variations of seismic waves. In applying the coda wave method, firstly, a type curve representing the average pattern of the individual coda decay curves for 0.75, 1.5, 3.0, 6.0, 12.0, and 24.0 Hz values was estimated. Secondly, lateral variation of coda Q and the attenuation coefficients for three main tectonic patterns are estimated. The shape of the type curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The Q _o and η values vary from 30 to 180 and from 0.55 to 1.25, respectively for SW Anatolia. In SW Anatolia, coda Q–f relation is described by and δ = 0.008 km⁻¹. These results are expected to help in understanding the degree of tectonic complexity of the crust in SW Anatolia.     

An Adaptive Wavenumber Sampling Strategy for 2.5D Seismic-Wave Modeling in the Frequency Domain

Simulation of seismic waves from a 3D point-source in a 2D medium may be performed in the frequency-wavenumber domain (called 2.5D modelling). It involves computing the Fourier-transformed Green's function for a number of frequency (ω) and strike direction wavenumber (k_y) values and doubly inverse transforming to convert to the traveltime and distance space. Such modeling produces a wavefield with 3D features but the computation becomes pseudo 2D (i.e., in the xz-plane) rather than 3D (in the xyz-frame). The common sampling strategy for the wavenumber is inefficient for 2.5D wave modeling because it employs a large number of wavenumbers (k_y). This leads to a high cost of computer time in the linear-equation-solving processing, which detracts from the advantages of 2.5D modeling. In this paper, we use two analytic frequency-wavenumber-domain solutions for seismic waves in a homogeneous medium and an inhomogeneous media (two semi-infinite media in contact) to investigate the properties of the solutions and an efficient sampling strategy for choosing the wavenumbers. We have carried out analytic and numerical experiments with these solutions, and present adaptive Gauss–Legendre abscissae for the wavenumber sampling in terms of a modeling situation. We show that the effective range and the number of sampling points of the wavenumber define the adaptive sampling strategy, and they can be estimated in terms of the wavelength and the maximum source-receiver offset. We apply this sampling strategy to the finite-element method and demonstrate that the range and number of sampling points may be adapted for obtaining significant computational efficiency and satisfactory accuracy for every frequency component. Such 2.5D wave modeling can be readily applied for frequency-domain full-waveform inversion for seismic surface measurements and crosshole seismic waveform tomography.     

Nonlinear dynamics of 3D beams of fast magnetosonic waves propagating in the ionospheric and magnetospheric plasma

On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B _~/B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4πnT/B ² ? 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = (B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.     

Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves

The efficiency of energetic electron cyclotron acceleration in the Earth’s magnetosphere in different regimes of electron resonant interaction with parallel propagating whistler mode waves of variable frequency, specifically, with chorus ELF-VLF emissions, is considered. The regime of stochastic acceleration, typical of the interaction between particles and noise-like emissions, and particle acceleration in the regime of nonlinear trapping by a quasimonochromatic wave field are discussed. The specific feature of the latter regime consists in its non-diffuse character, i.e., the definite sign of the energy variation depending on the frequency variation in the wave packet. The trapped electron energy becomes higher if frequency increases within an element, which is typical of chorus emissions. For the parameters typical of chorus emissions (the amplitude of a wave magnetic field B _～ = 10² nT, the initial frequency ω ～ 0.3ω _H , and the frequency variation &;Dω ～ 0.15ω _H , where ω _H is the electron gyrofrequency), the energy increase during one act of such an interaction at L = 4?5 exceeds the rms variation in the energy of untrapped electron (during stochastic acceleration) by one-two orders of magnitude. The estimates indicate that a considerable fraction (several tens of percent) of the chorus element energy can be absorbed by electrons accelerated in the trapping regime during a single hop.     

The Q value variations in the preparing process of rock rupture

In this paper, the "spectral amplitude ratio method" (SAR), "energy method" (EN) and "coda wave method" (CW) are used to calculate theQ value variations of gneiss in the preparing rupture process. The obtained results show that the variation state ofQ values by SAR features the shape of relative stability—gradual increment to the maximum—then decrement and final rupture. The variation state ofQ values by EN is just contrary to that by SAR, i. e. with the shape of stability—decrement—increment—and final rupture. The varation state ofQ values by CW is similar to that by EN, its main frequency features the shape of relatively high value—decrement to the minimum—increment—and final rupture. But to the high frequency (higher than the main frequency), the variation state ofQ values features the shape of the stable value-increment to the maximum-decrement-and final rupture. At the same time, the results by coda wave amplitude spectrum show that, when stress reaches 70% of rupture stress, the high frequency component of S wave rapidly reduces (Q _c increasing); at the time of impending the main rupture, the main frequency component reduces with a large scale (Q _c increasing again), this may be the reason which causes the different variation states of two codaQ values. The result of amplitude spectra of P, S (initial wave) waves also show that with the appearance of microcracks the frequency band of S wave turn to be narrow, the high frequency component is reduced quickly, i. e. the S wave spectra have different variation states with different frequency components. That is why theQ _s obtained by different methods have different variation characteristics.