Wave Normal Direction Research Articles

Polarization measurement of Auroral Kilometric Radiation by INTERBALL-2 satellite

Preliminary analyses of low and high resolution data are presented from the polar plasma waves measured on board INTERBALL-2 satellite in three frequency bands: ELF (5–1000 Hz), VLF(1–20 kHz) and LF (20–260 kHz). The propagation and polarization characteristics of the Auroral Kilometric Radiation (AKR) emission are estimated and studied. The obtained result shows that R-X and L-O modes of AKR emission just above source regions are found. The propagation characteristics are also determined: wave normal directions weakly oblique or quasi-parallel to the earth magnetic field direction.

Guiding of whistler-mode waves with frequencies above one half of the gyrofrequency in the magnetosphere

Ray-tracing calculations show that a trough, L = 4.6, located in the region outside the plasmapause is capable to guide whistler-mode waves in frequency range 0.5fBmin?0.64fBmin, from one hemisphere to the other. From an initial position rays propagate in unducted mode up to h ? 14000 km where they are trapped inside the trough. Propagation along the trough is possible only with great shifting of wave normal direction in respect to the direction of the geomagnetic induction B, following the variations of the magnitude of the ambiental geomagnetic induction, or those of ratio f/fB. On leaving the trough rays propagate in unducted mode downward in the magnetosphere.

Preliminary results from the MEMO multicomponent measurements of waves on-board INTERBALL 2

Abstract. The MEMO (MEsure Multicomposante des Ondes) experiment is a part of the INTERBALL 2 wave consortium. It is connected to a total of six electric and nine magnetic independent sensors. It provides waveforms associated with the measurement of two to five components in three frequency bands: ELF (5–1000 Hz), VLF (1–20 kHz), LF (20–250 kHz). Preliminary analyses of low and high resolution data are presented. The emphasis is put on the estimation of the propagation characteristics of the observed waves.VLF hiss emissions are shown to be mainly whistler mode emissions, but other modes are present. An accurate estimation of the local plasma frequency is proposed when the low L = 0 cutoff frequency is identified. AKR emissions observed just above source regions are studied. R-X and L-O modes are found: the first at the lowest frequencies and the second at the highest. Both propagate with wave normal directions weakly oblique or quasi-parallel to the Earth's magnetic field direction. Propagation characteristics are also determined for a (non-drifting) fine structure of AKR. There is no fundamental difference with structurless events. Nightside and dayside bursts of ELF electromagnetic emissions are presented. It is not clear whether the two emissions belong to the "lion roar" emissions or not.Key words. Magnetospheric physics (auroral phenomena; plasma waves and instabilities; instruments and techniques)

Global electron density distribution in the plasmasphere deduced from Akebono wave data and the IRI model

Abstract Determination of global electron density distribution in the plasmasphere has been attempted using the wave normal directions and delay time of Omega signals, and in-situ electron density observed on the Akebono satellite. The present study is based on the assumption that the plasma model is represented by a diffusive equilibrium (DE) model with temperature gradient along a magnetic field line, and that the electron density at a reference altitude (1000km) is dependent on L-value. Relative concentrations of ion constituents H+, He+, and O+ at the reference altitude are determined by fitting as either L-independent or L-dependent. For the altitude range below the reference altitude, we have adopted a distribution which has one maximum density at the F2 peak and one minimum density at the E valley, both being referred to the IRI model. The parameters related to these models are determined by the non-linear least squares fitting method for the in-situ electron density, the wave normal direction and the delay time of Omega signals observed by Akebono. Wave normal directions and delay time at Akebono for the model are determined by ray tracing. The validity of our plasmaspheric model based on the DE model was checked by comparing it with the SUPIM (Sheffield University Plasmaspheric and Ionospheric Model), and we can conclude that our model is flexible enough to represent the general global distributions of the electron density in the plasmasphere, although it is possible that in some cases, unrealistic distributions of the plasma temperatures should be used in the model. The reliability of our fitting algorithm was also checked by computer simulations, and we have confirmed that the global electron density distribution can be determined from the satellite wave data, without any significant error. Several plasmaspheric electron density distributions are shown as a result of applying our method to Akebono data.

Ray tracing study of whistlers guided by a field-aligned depression of electron density in the magnetosphere

The properties of VLF waves guided by a field-aligned depression of electron density in different models of the magnetosphere are studied. Ray tracing calculations show that the guidance of VLF waves from one hemisphere to the other is made possible by the existence of Gaussian cross-section trough. The guidance of VLF waves occurs only at the inner side of the trough, when it is located at L ⩽ 2.2 and L ⩾ 4.0 for the winter night model and at L ⩾ 1.5 for the summer day model of the magnetosphere. All analyzed troughs are modelled with the same electron density depression of 15% and with the effective width of 215 km in the equatorial plane. Initial latitude ranges for various wave normal directions, from which rays are successfully guided, are moved equatorward from the trough centre. For one trough the initial latitude ranges are defined so that corresponding rays reach 300 km altitude in the conjugate hemisphere with a final wave normal angle inside the ionospheric transmission cone. The guidance of VLF waves by a trough is possible in a para-longitudinal mode or a gradient trapping mode, depending on initial positions. Changing these positions, there is a continuous transition from one ray path to the other. The main difference in the characteristics of rays guided in a para-longitudinal mode and a gradient trapping mode is the behaviour of the wave normal angle to the geomagnetic field. A para-longitudinal mode has lower value of this parameter than a gradient trapping mode. A ray guided in a gradient trapping mode deeply enters a trough. A slight difference of latitudinal gradients of the geomagnetic field and electron density in the lower altitude magnetosphere is responsible for determining a type of mode for guiding whistlers by a trough. These whistlers are characterized by an upper cut-off frequency which is almost 0.5 ƒBmin.

Doppler shift pulsations on whistler mode signals from a VLF transmitter

Whistler mode signals from the NAA transmitter (24 kHz) received at Faraday, Antarctica are processed to obtain the Doppler shift at a much higher time resolution than has previously been possible. This has allowed the observation of pulsations of about 13 mHz frequency which are believed to be associated with hydromagnetic waves in the magnetosphere. The pulsations are observed separately on signals with a number of discrete group delay features that can be interpreted as individual whistler ducts. Using the measured pulsation phase over the array of ducts the phase velocity and wave normal direction of the hydromagnetic wave in the equatorial plane are estimated. The direction of propagation is consistent with a source on the dayside magnetopause. The association between whistler mode Doppler shifts and hydromagnetic waves has been reported before but not, as far as we are aware, using an experimental technique that allows measurements on individual ducts in order to determine the direction of propagation of the hydromagnetic wave.

Electron density distribution in the plasmasphere in conjunction with IRI model, deduced from Akebono wave data

Determination of electron density distribution in the plasmasphere has been attempted using wave normal directions and delay time of Omega signals, and in-situ electron density observed on the Akebono satellite /1/, /2/. The present study is based on the assumption that the plasma model is represented by a diffusive equilibrium (DE) model with a vertical temperature gradient, and the electron density at a reference altitude (1000km) being dependent on the L value. The parameters related to these models were determined by non-linear least square fitting of the in-situ electron density, the wave normal direction and delay time of Omega signals observed by Akebono. Relative concentrations of ion constituents of H +, He +, O + at the reference altitude are determined by fitting as either L independent or L dependent. Connecting the global plasmaspheric density model with IRI in the ionospheric altitude is also tried.

Analysis of Wave Normal and Poynting Vectors of the Chorus Emissions Observed by GEOTAIL.

Many chorus emissions were observed in the frequency range from 200 Hz to 1 kHz when the GEOTAIL spacecraft was skimming inside the dayside magnetopause. The Wave Form Capture (WFC) onboard GEOTAIL obtained simultaneous wave forms of two electric and three magnetic components of the emissions. Spectral structures of the chorus emissions observed by the WFC are roughly classified into four types: rising tone, falling tone, hook, and structureless. In this paper, as a preliminary report, the wave normal directions for each type of the emissions except for the structureless are derived by the Means' method around the geomagnetic field line to know their propagation characteristics. In addition, Poynting directions of the chorus emissions are derived by using their five electromagnetic components. Derived propagation directions of the chorus emissions along a GEOTAIL orbit indicate that they are generated around the dayside geomagnetic equator, which is consistent with the well-known model of chorus generation through cyclotron resonance in the dayside outer magnetosphere.

K-vector determination of whistler mode signals by using amplitude data obtained by a spacecraft borne instrument

A straightforward method for determination of k-vector (wave normal) direction of a whistler mode signal observed onboard spacecraft consists in measuring three components of the wave magnetic field with their instantaneous amplitudes and phases. In that method, one needs to send by telemetry a total wave form of a signal, which requires much larger bandwidth than for sending amplitudes only. The present study develops another method of determination of the wave normal direction based only on the amplitude data; the method is checked using Omega signal observations by the Akebono satellite. It should, however, be noted that the sense of k-vector is not determined by this proposed method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Determination of electron density distributions in the plasmasphere by using wave data observed by Akebono satellite

Determination of electron density distribution in the plasmasphere has been attempted using wave normal directions and delay time of Omega signals observed on the Akebono satellite as well as the electron density along the satellite trajectory.

Propagation Characteristics of Auroral Hiss Observed by Akebono Satellite.

V-shaped hiss and saucer emission observed by the Akebono satellite in the auroral region in the altitude range between 3, 000 km and 5, 000 km were studied on their wave normal directions using 5 components of electric and magnetic field wave data by Phillips-Tikhonov regularization method. It was found that the V-shaped hiss come down to the spacecraft and their azimuthal direction of wave normal is anti-symmetric with respect to the location of V-shaped frequency minimum. Ray tracing study is made to see how the frequency versus time characteristics and wave normal direction of the emissions should be at the satellite level. The results by ray tracing shows good agreement with the observation, under the assumption that the initial wave normal direction is circularly symmetric around the magnetic field, with the resonance cone angle.

Excitation of electromagnetic waves by delta function current sheets in the ionospheric plasma

The excitation of electromagnetic wave packets by delta function current sheets in a dispersive magnetoplasma is studied, in which the wave normal direction is vertical to the current sheet but the Earth's magnetic field is assumed to have an arbitrary direction to the wave normal direction. The temporal and spatial evolution of wave packets in the ionospheric F2 plasma layer is analyzed by an exact numerical inversion method of the Laplace transform. Properties of these excited waves are discussed in different frequency bands; (1) quasi‐free space modes, (2) whistler mode, and (3) hydromagnetic wave modes. By interpreting the waveforms at fixed points in the plasma as experimental data, the obtained results provide explicit information about the nature of the transient response, and this can be used as a diagnostic technique of the plasma.

Propagation characteristics of the ELF emissions observed by the satellite Akebono in the magnetic equatorial region

Emissions with their frequencies below 100 Hz are often observed by the Akebono satellite in the vicinity of the geomagnetic equatorial plane. These ELF emissions are classified into two types: One is an ion cyclotron wave below the local proton cyclotron frequency and the other is assumed to be magnetosonic wave observed not only below but also above the local proton cyclotron frequency. The wave normal directions of the latter type of emissions were estimated by using the wave distribution function method. It is found that the emissions are propagating with their wave normal direction nearly perpendicular to the meridian plane. The propagation characteristics of these emissions are also examined by ray tracing including the effects of ions. The ray tracing study clarified that the wave can propagate around the plasmapause because of the trapping effect of density gradient. In this paper we propose that these emissions are generated just outside the plasmapause and are propagating around the plasmapause with their wave normal nearly perpendicular to the geomagnetic field line and to the meridian plane.

Green dyadic and dipole fields for a medium with anisotropic chirality

A closed-form expression is derived for the Green dyadic corresponding to a reciprocal bianisotropic medium with isotropic permittivity and permeability and arbitrary anisotropic chirality. Such a medium can be approximated, for example, by inserting in an isotropic host medium an equal number of similar right- and left-handed metal helices with suitable orientations. The solution is applied to determine the electric field of an electric dipole embedded in such a medium. Evaluation of its far-field shows that the wave is split into two plane waves with different wave-normal directions.

Ray‐tracing studies of the arrival direction and the ionospheric penetration of whistlers at low latitudes

Direction‐finding measurements of whistlers on the ground at low latitudes reveal that whistlers arrive from narrow regions of the zenith of only a few tens of kilometers in diameter. Using an appropriate geomagnetic field model and an ionospheric model including a field‐aligned duct, the characteristics of the arrival direction of low‐latitude whistlers are studied. Wave normal directions at the duct exit are calculated for whistler waves initially injected vertically upward at the conjugate duct entrance. Vertically downward wave normals appear at the duct exit quasi‐periodically for the injection positions at the duct entrance. Thus the whistler duct operates to direct the wave normal of whistlers at the duct exit vertically downward and make ionospheric penetration easier. The mechanism of this penetration is investigated comparing the observed characteristics of the arrival direction with the ray‐tracing calculations. The whistler energy emitted from the duct exit reaches the bottom of the ionosphere without spreading and then is radiated into free space from there. The heights of the conjugate duct ends at low latitudes are concluded to extend downward in the bottomside ionosphere for most ground whistlers. These results may be significant also for the study of ground whistlers at higher latitudes.

Low‐Mach number quasi‐parallel shocks: Upstream waves

The structure of a low Mach number (Alfvén Mach number MA = 2.2) quasi‐parallel shocks is investigated using a two‐dimensional hybrid (particle ions, massless fluid electrons) code. We have run cases with average magnetic field ‐ shock normal angles of ΘBno = 20°, 30°, and 45°. Initially, phase standing dispersive whistler waves with an upstream directed group velocity are radiated by the shock ramp. As expected, the wave vector of these whistler waves is parallel to the average shock normal direction. The steepness of the shock ramp varies along the shock surface; this leads to a modulation of the whistler wave amplitude at a constant phase, i.e., perpendicular to the wave vector. Subsequently, ions are backstreaming from the shock into the upstream medium. At ΘBno = 30° these ions excite, as in the one‐dimensional hybrid simulations by Omidi et al. (1990), longer wavelength whistler waves by an electromagnetic ion/ion beam instability. The wave normal of these longer wavelength whistler waves is in between the average magnetic field direction and the shock normal. The skewing of the wave normal into the shock normal direction is attributed to a large density gradient of backstreaming ions upstream of the shock ramp in the shock normal direction. At ΘBno = 20° the shock consists of whistlers in the upstream, whose wavelength and shock directed phase velocity increases gradually toward the shock. It is suggested that in this more parallel case remnants of the dispersive whistlers continue to exist further upstream and interact with backstreaming ions. This leads to a change of the wave normal direction as the waves are convected toward the shock. In the 45° case the upstream density of backstreaming ions is greatly reduced. Only close to the shock ramp (within ∼ 5c/ωpi) does the backstreaming ion density exceed 10% of the solar wind density. Wave vectors of small wavelength whistlers in this region are almost aligned with the shock normal.

Electron density profile in the magnetosphere deduced from in situ electron density and wave normal directions of omega signals observed by the Akebono (EXOS D) satellite

We describe a new method to construct the global plasma distribution in the plasmasphere using the electron density measured along the trajectory of the Akebono (EXOS D) satellite and the wave normal direction of Omega signals simultaneously observed by the same spacecraft. In this method the plasma density distribution is described by using the diffusive equilibrium model, with eight parameters, that is, die relative abundances and temperatures of ions, and the electron density at a reference altitude. This model is first fit in a least squares sense to the electron density observed along the spacecraft trajectory. The fit solution is not always unique. In such cases it is necessary to constrain the possible solutions further. Therefore we ray trace Omega signals from their source location and check if the wave normal directions at the spacecraft location are consistent with those observed. We present here three different examples of fitting methods in which fixed, freely fitted, and constrained fitted parameters yield reasonable plasma distributions.

Whistlers and plasmaspheric hiss: Wave directions and three‐dimensional propagation

Wave data from the DE 1 satellite showing simultaneously nonducted whistlers and hiss are analyzed to determine wave propagation directions. At L = 3.8 and a geographic latitude of λg = 12°S, the average wave normal directions of discrete whistlers are measured to be ∼51° for fnof;= 4.5 kHz and ∼60° for fnof;= 3.5 kHz, forming a small (&lt;20°) angle with the magnetic meridional plane. Hiss wave normal angles are determined as ∼70° and ∼77° for ƒ = 3.5 kHz and fnof; = 2.5 kHz, respectively, with the wave vector being almost perpendicular to the meridional plane. While the measured wave normal angles of whistlers and hiss are consistent with generation of hiss by magnetospheric whistlers, existence of a significant azimuthal component indicates that further assessment of this connection must be based on three‐dimensional ray tracing. A new approximate analytical formulation of three‐dimensional propagation of whistler waves is developed and used to model the drift of magnetospherically reflected whistlers in azimuth. The results show that depending on initial parameters, the time of arrival of whistler rays at a fixed observation point can differ by 10 ‐ 20 s, with signals from different magnetospherically reflected whistlers overlapping to evolve into a hiss like signal. The total azimuthal drift of whistler rays is found to not exceed ∼30°, so that plasmaspheric hiss may be produced by nonducted whistlers at longitudes correlated with the location of thunderstorm activity.

Characteristics of the coupled Z mode at Arecibo

For propagation in the magnetic meridian plane at two particular angles of incidence near the vertical, the ordinary (O) electromagnetic mode couples into what Budden [1961] calls the extraordinary (X) mode and what more recently has been called the Z mode. One of the angles is northward of zenith and one is southward. These angles form the transition between O mode reflections at a “Spitze” where the wave frequency ω matches the plasma frequency ωp and reflection below the height where ω = ωp. If the O mode propagates southward from Arecibo, the coupled Z mode is reflected up to a few kilometers above the height of the Spitze; it then propagates downward through the Spitze height to a height where the group path is horizontal. Assuming a horizontal, plane‐stratified uniformly varying ionosphere and no nonlinear effects, the refractive index and wavenormal direction approach constant finite values at this height and the wave remains electromagnetic in character; this is a new result which has not been previously reported. The group velocity is small, and the wave becomes heavily damped due to electron‐ion collisions after several milliseconds. If the O wave propagates northward, the coupled Z mode is reflected a couple of hundred meters or less above the Spitze height; it then propagates downward through the Spitze height and approaches horizontally the height at which the Appleton‐Hartree refractive index becomes infinite. For the same above mentioned assumptions, the Z mode converts gradually from electromagnetic to electrostatic in nature. The electrostatic or Langmuir mode attains a small downward component of group velocity and propagates downward for a few tens of meters while being heavily damped by electron‐ion collisions. Neglecting damping and nonlinear effects, the intensity of the Z mode varies approximately inversely with group velocity. If the HF array near the Arecibo Observatory were modified to place the main or secondary beams in the coupling directions, the electric field due to the coupled Z wave could be enormous. Even weak transmissions from the array should produce a nonlinear region. It is thus difficult to say how much of the linear mode coupling description is valid before nonlinear effects dominate. The nonlinear effects might generate Langmuir waves of a similar frequency to the HF which could be detected by the Arecibo 430‐MHz radar. Exciting new plasma line observations should thus be possible.

Evidence for proton cyclotron waves near comet Giacobini‐Zinner

We have computed frequency spectra of power density and polarization parameters of magnetohydrodynamic waves from observations on board the ICE spacecraft as it flew past comet Giacobini‐Zinner on September 11, 1985. Since the spectral parameters are frequency dependent, we find that the analysis is best carried out in a ‘wave’ reference frame where one of the major axes is along the wave normal direction for each frequency component. The power density along the wave normal direction shows a systematic peak structure which we identify as belonging to cyclotron wave harmonics of pick‐up ions (H+, H2+, and O+) near the comet. The fundamental harmonics of the cyclotron waves are also consistent with the gyrofrequencies calculated from the magnetic field data.