Wave Normal Vector Research Articles

Energy Transfer Between Various Electron Populations Via Resonant Interaction With Whistler Mode Wave

AbstractElectron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi‐monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave‐particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles.

Critical Angle Formulation of Nonuniform Plane Waves for Determining Correct Refraction Angles at Planar Interface

The expressions and properties of the critical angles of nonuniform plane waves for determining the correct refraction angle at the infinite planar interface of two linear, isotropic, and homogeneous media are presented. The two media could be lossless or lossy. For the case where the complex wave vector of Adler–Chu–Fano formulation and the normal vector to the interface are coplanar, a critical angle equation, which is simpler than the extant one, under the condition that one or two critical angles exist, is formulated. In addition, for the case where the complex wave vector and normal vector to the interface are noncoplanar, a critical angle equation is formulated, rendering the 3-D nonuniform plane wave refraction feasible for utilization in many areas of optics. The presented critical angle equations were validated for various nonuniform plane waves and media.

A Theory of Interaction Between Relativistic Electrons and Magnetospherically Reflected Whistlers

AbstractWhistlers that originate from lightning strokes are among the prevalent wave phenomena in the magnetosphere, which makes their interactions with magnetospheric plasma particles of particular importance. We develop a theory that takes into account the main features of this interaction, namely, the space‐time boundedness of wave packets representing magnetospherically reflected whistlers, and the variation of frequency, wave normal vector, and amplitude inside wave packets. We take into account the inhomogeneity of the ambient plasma and the geomagnetic field, as well as relativistic effects in particle dynamics. A particular emphasis is placed on energy exchange between resonant particles as an intrinsic component part of wave‐particle interaction in plasma.

U‐Shaped Spectrograms Registered by the DEMETER Satellite: Observational Features and Formation Mechanism

AbstractU‐shaped spectrograms observed by the DEMETER satellite in the equatorial region of the upper ionosphere are presented and explained for the first time. These spectra are characterized by the latitude‐dependent upper cutoff frequency that increases with the latitude during nighttime. The observations suggest that this very low frequency wave phenomenon is closely connected with the anomalous increase in cold plasma density at and below the satellite. We show that restricting the analysis to propagation effects is insufficient to explain U‐shaped spectra, and other effects, in particular, the collisional wave damping should be taken into consideration. To calculate the wave damping, we use the method of successive approximations. In the first approximation, we calculate the ray trajectory and the wave normal vector along it, using the equations of geometrical optics neglecting collisions. In the second approximation we calculate the collisional wave damping along the precalculated trajectory. We show that the effects of very low frequency wave propagation and attenuation in the equatorial region of the upper ionosphere explain the main features of the phenomenon under discussion.

Magnetic Search Coil (MSC) of Plasma Wave Experiment (PWE) aboard the Arase (ERG) satellite

This paper presents detailed performance values of the Magnetic Search Coil (MSC) that is part of the Plasma Wave Experiment on board the Arase (ERG) satellite. The MSC consists of a three-axis search coil magnetometer with a 200-mm-long magnetic core. The MSC plays a central role in the magnetic field observations, particularly for whistler mode chorus and hiss waves in a few kHz frequency range, which may cause local acceleration and/or rapid loss of radiation belt electrons. Accordingly, the MSC was carefully designed and developed to operate well in harsh radiation environments. To ascertain the wave-normal vectors, polarizations, and refractive indices of the plasma waves in a wide frequency band, the output signals detected by the MSC are fed into the two different wave receivers: one is the WaveForm Capture/Onboard Frequency Analyzer for waveform and spectrum observations in the frequency range from a few Hz up to 20 kHz, and the other is the High Frequency Analyzer for spectrum observations in the frequency range from 10 to 100 kHz. The noise equivalent magnetic induction of the MSC is 20,{hbox {fT/Hz}}^{1/2} at a frequency of 2 kHz, and the null depth of directionality is − 40 dB, which is equivalent to an angular error less than 1^{circ }. The MSC on board the Arase satellite is the first experiment using a current-sensitive preamplifier for probing the plasma waves in the radiation belts.

Examining Coherency Scales, Substructure, and Propagation of Whistler Mode Chorus Elements With Magnetospheric Multiscale (MMS)

AbstractWhistler mode chorus waves are a naturally occurring electromagnetic emission observed in Earth's magnetosphere. Here, for the first time, data from NASA's Magnetospheric Multiscale (MMS) mission were used to analyze chorus waves in detail, including the calculation of chorus wave normal vectors, k. A case study was examined from a period of substorm activity around the time of a conjunction between the MMS constellation and NASA's Van Allen Probes mission on 07 April 2016. Chorus wave activity was simultaneously observed by all six spacecraft over a broad range of L shells (5.5 < L < 8.5), magnetic local time (06:00 < MLT < 09:00), and magnetic latitude (−32° < MLAT < −15°), implying a large chorus active region. Eight chorus elements and their substructure were analyzed in detail with MMS. These chorus elements were all lower band and rising tone emissions, right‐handed and nearly circularly polarized, and propagating away from the magnetic equator when they were observed at MMS (MLAT~−31°). Most of the elements had “hook”‐like signatures on their wave power spectra, characterized by enhanced wave power at flat or falling frequency following the peak, and all the elements exhibited complex and well‐organized substructure observed consistently at all four MMS spacecraft at separations up to 70 km (60 km perpendicular and 38 km parallel to the background magnetic field). The waveforms in field‐aligned coordinates also demonstrated that these waves were all phase coherent, allowing for the direct calculation of k. Error estimates on calculated k revealed that the plane wave approximation was valid for six of the eight elements and most of the subelements. The wave normal vectors were within 20–30° from the direction antiparallel to the background field for all elements and changed from subelement to subelement through at least two of the eight elements. The azimuthal angle of k in the perpendicular plane was oriented earthward and was oblique to that of the Poynting vector, which has implications for the validity of cold plasma theory.

Spaced‐based search coil magnetometers

AbstractSearch coil magnetometers are one of the primary tools used to study the magnetic component of low‐frequency electromagnetic waves in space. Their relatively small size, mass, and power consumption, coupled with a good frequency range and sensitivity, make them ideal for spaceflight applications. The basic design of a search coil magnetometer consists of many thousands of turns of wire wound on a high permeability core. When a time‐varying magnetic field passes through the coil, a time‐varying voltage is induced due to Faraday's law of magnetic induction. The output of the coil is usually attached to a preamplifier, which amplifies the induced voltage and conditions the signal for transmission to the main electronics (usually a low‐frequency radio receiver). Search coil magnetometers are usually used in conjunction with electric field antenna to measure electromagnetic plasma waves in the frequency range of a few hertz to a few tens of kilohertzs. Search coil magnetometers are used to determine the properties of waves, such as comparing the relative electric and magnetic field amplitudes of the waves, or to investigate wave propagation parameters, such as Poynting flux and wave normal vectors. On a spinning spacecraft, they are also sometimes used to determine the background magnetic field. This paper presents some of the basic design criteria of search coil magnetometers and discusses design characteristics of sensors flown on a number of spacecraft.

Specific features of VLF wave propagation in the earth’s inner magnetosphere

The ray trajectories of waves in the very low frequency (VLF) range in the case of nonducted propagation in the earth’s inner magnetosphere are studied as functions of location of their source region, frequency, and initial angle between the vector of wave normal and intensity vector of external magnetic field. Simulation is performed on the basis of geometric ray tracing approach in multicomponent plasma. The parameters of the magnetospheric medium were calculated using a diffusion model of the concentration distribution of plasma components and the International Geomagnetic Reference Field (IGRF) model. It is shown that the magnetospheric wave reflection can occur if the lower hybrid resonance frequency is greater than its own wave frequency (ωLHF > ω), i.e., at the latitudes λ ≈ 50°. The simulation results confirm that the quasi-longitudinal approximation cannot be used to describe the magnetospheric whistler propagation. We present simulations of propagation of chorus-type wave magnetospheric emissions that were performed using realistic wave distributions over initial parameters. In particular, we present distributions of chorus waves over directions of wave vector as functions of geomagnetic latitude; these distributions are required to study the particle scattering and acceleration processes in the radiation belts. Our results well agree with CLUSTER satellite measurements.

Characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves observed on THEMIS

The characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves outside the plasmapause are investigated for the lower (0.1–0.5 fce) and upper bands (0.5–0.8 fce), where fce is the equatorial electron cyclotron frequency. To analyze the wave properties, we utilized high‐resolution waveform data from multiple THEMIS spacecraft in the near‐equatorial magnetosphere from June 2008 to November 2012. Full measurements of the wave electric and magnetic fields are used to calculate the Poynting fluxes and construct the wave normal vectors, which are then used to calculate the polar and azimuthal angles with respect to the background magnetic field. Statistical results show that the majority of whistler‐mode waves propagate away from the magnetic equator, suggesting that the major source region is very close to the equator. The lower band wave normal angle distribution shows a major peak close to the field line direction and a secondary peak near the resonance cone. In contrast, the wave normal distribution of upper band waves exhibits a broad distribution between 0° and 60° with the largest probability at ~0°. The azimuthal component of the wave normal vector predominantly points radially outward for both lower and upper band waves, but a tendency for azimuthal propagation is observed for lower band waves in the day and dusk sectors probably due to pronounced azimuthal density gradients in the afternoon sector. Our statistical results provide crucial information on the Poynting fluxes and wave normal vectors of whistler‐mode waves, which play a significant role in radiation belt electron dynamics.

Observations of chorus at Saturn using the Cassini Radio and Plasma Wave Science instrument

Observations at Saturn of whistler mode chorus emissions have been obtained by the Cassini Radio and Plasma Wave Science instrument. Data from the first 45 orbits are analyzed, and the characteristics of the chorus emissions are discussed. Wave normal and Poynting vector measurements from the five‐channel waveform receiver are used to examine the propagation characteristics of the chorus, and high‐resolution measurements from the wideband receiver are used to examine the fine structure. At Saturn, two different types of chorus are detected. The most common observations are of chorus propagating away from Saturn's magnetic equator, suggesting a source near the magnetic equator. This chorus is usually detected for many hours, is only observed below half the electron cyclotron frequency, and occurs primarily from L shells of about 5 to 8, and the occurrence of the emission shows no obvious correlation with Saturn magnetic latitude, longitude, or local time. The high‐resolution measurements show that the fine structure of this chorus typically consists of larger time scale features (many seconds to minutes) than detected at the Earth (<1 s). The second region of chorus detected at Saturn is in association with local plasma injections. For many of the plasma injection events, chorus emissions are detected both above and below half the electron cyclotron frequency, with a gap in the emission at half the cyclotron frequency. This chorus also shows fine structure at smaller time scales (<1 s to a few seconds), and the overall structure of this chorus appears more similar to chorus detected at the Earth.

Optical transverse excitation in quaterthiophene crystals by ultraviolet-visible internal and attenuated total reflection

We report internal and attenuated total reflection of light at the interface between glass and a quaterthiophene crystal in the spectral region of the electronic transitions. The bands corresponding to the absorption of the a(u) and b(u) Frenkel exciton states are detected for different polarization of the incident light. In particular, the wave-normal vector being almost perpendicular to the b(u) transition dipole moment allows its transverse component to be accessed, whose excitation in conventional external reflection or transmission spectroscopies is forbidden.

Absorption and propagation of light in quaterthiophene crystals

We examine absorption of light in quaterthiophene crystals for different directions of the ray and wave-normal vector after refraction on the vacuum/crystal interface. Experimental non-normal incidence spectra are reported where different absorption bands show different behaviour as a function of the angle of incidence. This allows to identify those originating from the b u Frenkel exciton state.

L dependence of energetic electron precipitation driven by magnetospherically reflecting whistler waves

Ray tracing analysis and a first‐order treatment of the wave frequency and electron energy dependence of gyroresonant pitch angle scattering reveals the L shell dependence of the time‐integrated energetic electron (>150 keV) precipitation flux in the drift loss cone due to a single cloud‐to‐ground lightning stroke. Primary features of the L dependence are determined by the ray paths of magnetospherically reflecting nonducted whistler waves, as well as the refraction of the wave normal vectors due to ionospheric horizontal electron density gradients at low latitudes. Calculations for lightning source latitudes of 25°, 35°, and 45°, with an assumed “average” ionospheric electron density profile, as well as an International Reference Ionosphere model profile, indicate that horizontal ionospheric electron density gradients can cause the whistler wave energy to focus near the geomagnetic equator on the first magnetospheric traverse, resulting in a spatially narrow precipitation signature at low L shells (1.4 < L < 1.65). The magnitude of this low‐L peak is found to be sensitively dependent on the local ionospheric density gradients. Subsequent magnetospheric reflections result in a broad precipitation peak at higher L shells (1.8 < L < 4.2), which is robustly present, with magnitude being relatively insensitive to lightning source‐latitude and ionospheric horizontal gradients. The calculated L dependences were found to be in excellent agreement with drift‐loss cone fluxes measured aboard the SAMPEX satellite.

Wave normal and Poynting vector calculations using the Cassini radio and plasma wave instrument

Wave normal and Poynting vector measurements from the Cassini radio and plasma wave instrument (RPWS) are used to examine the propagation characteristics of various plasma waves during the Earth flyby on August 18, 1999. Using the five‐channel waveform receiver (WFR), the wave normal vector is determined using the Means method for a lightning‐induced whistler, equatorial chorus, and a series of low‐frequency emissions observed while Cassini was in the magnetosheath. The Poynting vector for these emissions is also calculated from the five components measured by the WFR. The propagation characteristics of the lightning‐induced whistler were found to be consistent with the whistler wave mode of propagation, with propagation antiparallel to the magnetic field (southward) at Cassini. The sferic associated with this whistler was observed by both Cassini and the Stanford VLF group at the Palmer Station in Antarctica. Analysis of the arrival direction of the sferic at the Palmer Station suggests that the lightning stroke is in the same sector as Cassini. Chorus was observed very close (within a few degrees) to the magnetic equator during the flyby. The chorus was found to propagate primarily away from the magnetic equator and was observed to change direction as Cassini crossed the magnetic equator. This suggests that the source region of the chorus is very near the magnetic equator. The low‐frequency emission in the magnetosheath has many of the characteristics of lion roars. The average value of the angle between the wave normal vector and the local magnetic field was found to be 16°, and the emissions ranged in frequency from 0.19 to 0.75 ƒce, where ƒce is the electron cyclotron frequency. The wave normal vectors of these waves were primarily in one direction for each individual burst (either parallel or antiparallel to the local field) but varied in direction throughout the magnetosheath. This suggests that the sources of the emissions are far from the spacecraft and that there are multiple source regions.

EXOS-D (AKEBONO) very low frequency plasma wave instruments (VLF)

The Akebono (EXOS-D) satellite has been successfully observing the Earth's magnetosphere since it was launched on February 21, 1989. The objectives of VLF instruments on board the satellite were to investigate the behavior of plasma waves associated with accelerated auroral particles, wave-particle interaction mechanisms, and propagation characteristics of whistler-mode waves in the magnetosphere. The instruments measured not only the dynamic spectra of VLF waves up to 15 kHz by a wideband receiver, but also their absolute field intensities, wave normal vectors, and Poynting vectors. Two electric and three magnetic components with a bandwidth of about 50 Hz up to 12.5 kHz are sent to measure the wave normal vectors and Poynting vectors. The antenna impedance is measured to determine the correct absolute electric field intensities. The instruments have successfully measured the wave spectra, the wave normal vectors. Poynting vectors, the precise wave intensities, the antenna impedance, etc. The present paper describes the unique features of the instruments, especially the Poynting flux analyzers in more detail. Obtained scientific results are also reviewed.

An interpretation of a mysterious 3.0‐ to 4.6‐kHz emission band observed on Voyager 2 near Neptune

A whistler mode interpretation is provided for the narrowband signal (fnof; ∼ 3 – 4.6 kHz, Δfnof; ∼ 200 – 800 Hz) detected by the plasma wave instrument on Voyager 2 during its encounter with Neptune. Our analysis indicates that this signal may have been generated in a limited spatial region and that it propagated to other regions of the Neptunian magnetosphere in the nonducted whistler mode with wave normal vectors lying close to the whistler mode resonance cone. The observed frequency variation of the emission along the Voyager 2 trajectory is consistent with this interpretation. The source location is estimated to be near the magnetic equator at L ∼ 4 and dipole longitude of 111°W (260° W longitude in Neptune coordinate system). The source frequency and bandwidth are estimated to be 3.6 kHz and 300 Hz, respectively. The waves most likely would have been generated by energetic electrons with 2‐ to 20‐keV parallel energy via a gyroresonance mechanism. Our interpretation of the narrowband emissions places the following limits on the Neptunian thermal plasma density and temperature: (1) Ne,min > 0.16 el/cm3 for 1.2 RN < R < 5RN, (2) Ne,max=597.5 cm−3 at R = 1.3RN, (3) Te,max < 500–1000° K at R ∼ 5 RN. It is also possible that the weak UV aurora observed near Neptune could have been caused by the precipitation of energetic particles by the narrowband emission as a result of wave particle interactions.

Direction finding of radio sources in the ionosphere: Data bank structure and principle of resolution

The problem is direction finding of natural low-frequency radiation sources in the ionosphere, more specifically: to determine the distribution function of a set of wave normal vectors obtained by computing propagation between unknown sources and the (orbiting) receiver.

Electroelastic effect in alpha quartz

The electroelastic effect of α quartz is investigated by means of high-resolution measurements of ultrasonic transit times as a function of a superimposed biasing field. Experimental results are reported for 25 different configurations of wave normal, displacement, and electric field vectors. It is shown that these results may consistently by expressed in terms of an effective fifth-rank tensor with eight independent components.

Estimation of wave vector characteristics

In the realistic case of multiple electromagnetic plasma wave sources and multiple propagation paths, auto-correlation and cross-correlation products of the six wave components can be utilized to fit model parameters for the wave normal vector and Poynting vector distribution functions. With the complete wave vector characteristics, the wave mode can be identified, the index of refraction derived and the wave ray traced back towards the wave source region. Plasma wave instrumentation suitable for estimating some wave vector characteristics has been carried on satellites starting with FR-1 in 1964 and has evolved in various configurations on OGO-5, Injun-5, GEOS, Voyager, ISEE, Dynamics Explorer and the proposed OPEN spacecraft. Plasma wave research needs to advance along two parallel lines: (a) developing more sophisticated computer techniques for extracting the wave vector information from extensive data sets and (b) utilizing microprocessor technology in flight instruments to recognize specified phenomena and to capture the appropriate wave data for further on-board or ground processing.

On the minimum variance direction of magnetic field fluctuations in the azimuthal velocity structure of the solar wind

Studies of waves in the interplanetary medium often assume that the direction of minimum variance is parallel (or anti‐parallel) to the direction of the wave normal vector . In an azimuthally structured solar wind, geometrical optics predicts that the vectors of magneto‐hydrodynamic (MHD) waves should be refracted in a characteristic manner. The present study considers the properties of microscale magnetic field fluctuations for divers classes of large‐scale azimuthal velocity structures in the solar wind. Using 168.75 sec and 22.5 min variance matrices obtained by Mariner 5, we find that the direction of minimum variance does not exhibit any characteristic refraction pattern with respect to large scale velocity structures in the solar wind. The distribution of minimum variance directions is always strongly peaked at and symmetric about the average field direction, and shows no tendency to refract towards a more radial configuration. These observational results suggest that either the predictions of geometrical optics are incorrect, or that the direction of minimum variance is not indicative of the vector direction. We favor the latter interpretation.