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Ustinov, Andrey, Svetlana Khonina, and Alexey Porfirev. "Formation of Inverse Energy Flux in the Case of Diffraction of Linearly Polarized Radiation by Conventional and Generalized Spiral Phase Plates." Photonics 8, no. 7 (July 16, 2021): 283. http://dx.doi.org/10.3390/photonics8070283.
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Recently, there has been increased interest in the shaping of light fields with an inverse energy flux to guide optically trapped nano- and microparticles towards a radiation source. To generate inverse energy flux, non-uniformly polarized laser beams, especially higher-order cylindrical vector beams, are widely used. Here, we demonstrate the use of conventional and so-called generalized spiral phase plates for the formation of light fields with an inverse energy flux when they are illuminated with linearly polarized radiation. We present an analytical and numerical study of the longitudinal and transverse components of the Poynting vector. The conditions for maximizing the negative value of the real part of the longitudinal component of the Poynting vector are obtained.
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Janhunen, P., A. Olsson, N. A. Tsyganenko, C. T. Russell, H. Laakso, and L. G. Blomberg. "Statistics of a parallel Poynting vector in the auroral zone as a function of altitude using Polar EFI and MFE data and Astrid-2 EMMA data." Annales Geophysicae 23, no. 5 (July 28, 2005): 1797–806. http://dx.doi.org/10.5194/angeo-23-1797-2005.
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Abstract. We study the wave-related (AC) and static (DC) parallel Poynting vector (Poynting energy flux) as a function of altitude in auroral field lines using Polar EFI and MFE data. The study is statistical and contains 5 years of data in the altitude range 5000–30000 km. We verify the low altitude part of the results by comparison with earlier Astrid-2 EMMA Poynting vector statistics at 1000 km altitude. The EMMA data are also used to statistically compensate the Polar results for the missing zonal electric field component. We compare the Poynting vector with previous statistical DMSP satellite data concerning the electron precipitation power. We find that the AC Poynting vector (Alfvén-wave related Poynting vector) is statistically not sufficient to power auroral electron precipitation, although it may, for Kp>2, power 25–50% of it. The statistical AC Poynting vector also has a stepwise transition at R=4 RE, so that its amplitude increases with increasing altitude. We suggest that this corresponds to Alfvén waves being in Landau resonance with electrons, so that wave-induced electron acceleration takes place at this altitude range, which was earlier named the Alfvén Resonosphere (ARS). The DC Poynting vector is ~3 times larger than electron precipitation and corresponds mainly to ionospheric Joule heating. In the morning sector (02:00–06:00 MLT) we find that the DC Poynting vector has a nontrivial altitude profile such that it decreases by a factor of ~2 when moving upward from 3 to 4 RE radial distance. In other nightside MLT sectors the altitude profile is more uniform. The morning sector nontrivial altitude profile may be due to divergence of the perpendicular Poynting vector field at R=3–4 RE. Keywords. Magnetospheric physics (Auroral phenomena; Magnetosphere-ionosphere interactions) – Space plasma physics (Wave-particle interactions)
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Liu, Jihong, Jiangtao Su, and Hongqi Zhang. "The helicity, induced electric field and Poynting flux of AR 11158 and their relationship with the X-class flare." Proceedings of the International Astronomical Union 8, S294 (August 2012): 535–36. http://dx.doi.org/10.1017/s1743921313003104.
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AbstractWith the photospheric vector magnetic fields provided by SDO/HMI team, the helicity accumulation, induced electric field and Poynting flux is calculated for AR 11158 by using the local correlation tracking technique (LCT). It is found that the helicity accumulation reaches 6000×1040Mx2, the average densities of the induced electric field about 0.15-0.35 V cm−1, and that of the Poynting flux about 50-240 W m−2, within 50 hours. One main flare of X2.2 occurs in the increasing phase of the helicity accumulation, which also corresponds to the decreasing phase of the induced electric field and the gradual change phase of the Poynting flux. Before the flare, all these quantities increase rapidly for about 20 hours firstly, then increase gradually or even decrease for 8-9 hours.
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Domínguez, P. J., A. Gallegos, J. E. Macías-Díaz, and H. Vargas-Rodríguez. "Superenergy flux of Einstein–Rosen waves." International Journal of Modern Physics D 27, no. 07 (May 2018): 1850072. http://dx.doi.org/10.1142/s0218271818500724.
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In this work, we consider the propagation speed of the superenergy flux associated to the Einstein–Rosen cylindrical waves propagating in vacuum and over the background of the gravitational field of an infinitely long mass line distribution. The velocity of the flux is determined considering the reference frame in which the super-Poynting vector vanishes. This reference frame is then considered as comoving with the flux. The explicit expressions for the velocities are given with respect to a reference frame at rest with the symmetry axis.
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Franek, Jaroslav. "On Induction Heating - Conductor Excited by External Field." Journal of Electrical Engineering 64, no. 4 (June 1, 2013): 261–64. http://dx.doi.org/10.2478/jee-2013-0038.
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Electromagnetic field in a banded strip conductor excited by external AC voltage driven coil is analyzed. Inhomogeneous wave equation describing this axis-symmetrical configuration is deduced and solved to find the induced current density and the directional energy flux density (Poynting vector) in the conductor.
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Vinogradov, S. S., and A. V. Sulima. "Calculation of the poynting vector flux through a partially screened dielectric sphere." Radiophysics and Quantum Electronics 32, no. 2 (February 1989): 160–66. http://dx.doi.org/10.1007/bf01039672.
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Yan, Jia, and Thomas A. Dickens. "Reverse time migration angle gathers using Poynting vectors." GEOPHYSICS 81, no. 6 (November 2016): S511—S522. http://dx.doi.org/10.1190/geo2015-0703.1.
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Angle-domain common-image gathers provide much useful data about the subsurface, such as seismic velocities and amplitude-versus-angle (AVA) information, and they can be manipulated to provide high-quality stacked images. However, the computation of angle gathers for reverse time migration (RTM), the most physically accurate migration algorithm, has proven to be costly in terms of computer time and memory usage. We have developed an algorithm for computing RTM angle gathers in a relatively efficient manner. Our method is based on the construction of the directions of propagation of the source and receiver wavefields, given by the direction of energy flux, known as the Poynting vector. The computation is carried out in the space-time domain, avoiding the need to transform the wavefield to, for example, frequency-wavenumber space, as is needed for methods based on wavefront projection. Given accurate Poynting vectors for source and receiver wavefields, one may compute the local reflection angle and azimuth, as well as the reflector dip and azimuth. An important advantage of our method is that it is based on local direction information at the reflection point, and thus it avoids the loss of resolution and smearing that can occur with some other techniques. A simple implementation of the Poynting-vector method can lead to noisy gathers, with leakage between angle bins, caused by unstable division of the local wavefields. We have developed an efficient technique to mitigate this noise and evaluated examples illustrating the aforementioned smearing issues of the subsurface-offset-based gathers and the improvements in the Poynting-vector gathers arising from our algorithm enhancement. Finally, the use of angle gathers for AVA analysis requires that (relative) amplitudes as a function of angle be correct. To this end, we derive weight functions for computing gathers with the correct AVA behavior. We determine the correctness of these weights by testing them with synthetic data.
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Nalimov, A. G. "Energy flux of a vortex field focused using a secant gradient lens." Computer Optics 44, no. 5 (October 2020): 707–11. http://dx.doi.org/10.18287/2412-6179-co-688.
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In this paper we simulated the focusing of left circular polarized beam with a second order phase vortex and a second-order cylindrical vector beam by a gradient index Mikaelian lens. It was shown numerically, that there is an area with a negative Poynting vector projection on Z axis, that can be called an area with backward energy flow. Using a cylindrical hole in the output surface of the lens and optimizing it one can obtain a negative flow, which will be situated in the maximum intensity region, unlike to previous papers, in which such backward energy flow regions were situated in a shadow area. Thereby, this lens will work as an “optical magnet”, it will attract Rayleigh particles (with diameter about 1/20 of the wavelength) to its surface.
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Kotlyar, V. V., S. S. Stafeev, and A. A. Kovalev. "Sharp focusing of a light field with polarization and phase singularities of an arbitrary order." Computer Optics 43, no. 3 (June 2019): 337–46. http://dx.doi.org/10.18287/2412-6179-2019-43-3-337-346.
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Using the Richards-Wolf formalism, we obtain general expressions for all components of the electric and magnetic strength vectors near the sharp focus of an optical vortex with the topological charge m and nth-order azimuthal polarization. From these equations, simple consequences are derived for different values of m and n. If m=n>1, there is a non-zero intensity on the optical axis, like the one observed when focusing a vortex-free circularly polarized light field. If n=m+2, there is a reverse flux of light energy near the optical axis in the focal plane. The derived expressions can be used both for simulating the sharp focusing of optical fields with the double singularity (phase and polarization) and for a theoretical analysis of focal distributions of the intensity and the Poynting vector, allowing one to reveal the presence of rotational symmetry or the on-axis reverse energy flux, as well as the focal spot shape (a circle or a doughnut).
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Laitinen, T. V., T. I. Pulkkinen, M. Palmroth, P. Janhunen, and H. E. J. Koskinen. "The magnetotail reconnection region in a global MHD simulation." Annales Geophysicae 23, no. 12 (December 23, 2005): 3753–64. http://dx.doi.org/10.5194/angeo-23-3753-2005.
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Abstract. This work investigates the nature and the role of magnetic reconnection in a global magnetohydrodynamic simulation of the magnetosphere. We use the Gumics-4 simulation to study reconnection that occurs in the near-Earth region of the current sheet in the magnetotail. We locate the current sheet surface and the magnetic x-line that appears when reconnection starts. We illustrate the difference between quiet and active states of the reconnection region: variations in such quantities as the current sheet thickness, plasma flow velocities, and Poynting vector divergence are strong. A characteristic feature is strong asymmetry caused by non-perpendicular inflows. We determine the reconnection efficiency by the net rate of Poynting flux into the reconnection region. The reconnection efficiency in the simulation is directly proportional to the energy flux into the magnetosphere through the magnetopause: about half of all energy flowing through the magnetosphere is converted from an electromagnetic into a mechanical form in the reconnection region. Thus, the tail reconnection that is central to the magnetospheric circulation is directly driven; the tail does not exhibit a cycle of storage and rapid release of magnetic energy. We find similar behaviour of the tail in both synthetic and real event runs.
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Stafeev, S. S., and V. D. Zaitsev. "Focusing fractional-order cylindrical vector beams." Computer Optics 45, no. 2 (April 2021): 172–78. http://dx.doi.org/10.18287/2412-6179-co-805.
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By numerically simulating the sharp focusing of fractional-order vector beams (0≤m≤1, with azimuthal polarization at m=1 and linear polarization at m=0), it is shown that the shape of the intensity distribution in the focal spot changes from elliptical (m=0) to round (m=0.5) and ends up being annular (m=1). Meanwhile, the distribution pattern of the longitudinal component of the Poynting vector (energy flux) in the focal spot changes in a different way: from circular (m=0) to elliptical (m=0.5) and ends up being annular (m=1). The size of the focal spot at full width at half maximum of intensity for a first-order azimuthally polarized optical vortex (m=1) and numerical aperture NA=0.95 is found to be 0.46 of the incident wavelength, whereas the diameter of the on-axis energy flux for linearly polarized light (m=0) is 0.45 of the wavelength. Therefore, the answers to the questions: when the focal spot is round and when elliptical, or when the focal spot is minimal -- when focusing an azimuthally polarized vortex beam or a linearly polarized non-vortex beam, depend on whether we are considering the intensity at the focus or the energy flow. In another run of numerical simulation, we investigate the effect of the deviation of the beam order from m=2 (when an energy backflow is observed at the focal spot center). The reverse energy flow is shown to occur at the focal spot center until the beam order gets equal to m=1.55.
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Zhou, Hong, Xiao Ping Huang, Lei Zhong, Sheng Kang Ji, Yan Pang, Sheng Jie Bi, You Liang Liu, Kai Chen, and Feng Zhen Song. "Distribution of Electromagnetic Field and Energy Flux in the Thin Film Solar Cell with Silver Nano-Disk Array." Advanced Materials Research 669 (March 2013): 194–203. http://dx.doi.org/10.4028/www.scientific.net/amr.669.194.
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We simulate and calculate numerically the electromagnetic field and energy flux in single crystal silicon thin film solar cell coated with silver nano-disk square array by using the finite-difference time-domain (FDTD) method. Because of the surface plasmon resonance (SPR) of silver nano array, the electromagnetic field is redistributed and enhanced in the solar cell. The simulation results show that the electromagnetic field distribution and corresponding energy flux component depend on the nano array and the structure of absorbed layer in solar cell. The wavelength of the incident light relative to the nano array determine the profile of the electric field around the nano array. The electromagnetic field distribution in thin film is determined by the internal structure of solar cell. For different incident wavelengths, the electromagnetic field distribution in solar cell will changes. The energy flux named as Poynting vector also changes with the incident wavelength. To investigate the absorption of the solar cell, the normalized absorbed power at different wavelengths is calculated. Based on the SPR effect, the solar cell exhibts absorption enhancement sharply at a certain wavelength.
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Tang, Chen, and George A. McMechan. "The dynamically correct Poynting vector formulation for acoustic media with application in calculating multidirectional propagation vectors to produce angle gathers from reverse time migration." GEOPHYSICS 83, no. 4 (July 1, 2018): S365—S374. http://dx.doi.org/10.1190/geo2017-0331.1.
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The Poynting vector (PV) has been widely used to calculate propagation vectors of a pressure field (PF) in acoustic media. The most widely used acoustic PV formula is the negative of a product of the time and space derivatives. These two derivatives result in a phase shift between the PF and its PV; particularly, for a PF at a local magnitude peak, the PV modulus is zero and thus the propagation direction there is undefined. This “zero-modulus” issue is not consistent with the physical definition of the PV, which is the directional energy flux density of a PF because this definition indicates that the variation of the PV modulus should be consistent with the PF magnitude. This PV is only considered as kinematically correct and defined as K-PV. We derive the dynamically correct PV (D-PV) formula for acoustic media, which is the negative of the product of the reciprocal of the density, the PF itself, and a factor that is obtained by applying a time integration and a space derivative to the PF. There are two derivations. One uses the slowness vector, and the other is by simplifying the elastic PV. This D-PV does not suffer from the zero-modulus problem, and we also use it to update the multidirectional PV (MPV), which produces a D-MPV. Two strategies are provided to reduce the computational complexity of the time integration in the D-PV formula. Because the MPV already involves Fourier transforms between the time and frequency domains (which facilitates implementation of the time integration), its updated version causes only a very minor increase in the computational complexity of the original one. Numerical examples indicate that the D-PV provides more reliable propagation vectors than the K-PV, and the D-MPV provides more accurate angle-domain common-image gathers from reverse time migration of acoustic media than the K-MPV.
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Agapitov, O., V. Krasnoselskikh, Yu Zaliznyak, V. Angelopoulos, O. Le Contel, and G. Rolland. "Chorus source region localization in the Earth's outer magnetosphere using THEMIS measurements." Annales Geophysicae 28, no. 6 (June 25, 2010): 1377–86. http://dx.doi.org/10.5194/angeo-28-1377-2010.
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Abstract. Discrete ELF/VLF chorus emissions, the most intense electromagnetic plasma waves observed in the Earth's radiation belts and outer magnetosphere, are thought to propagate roughly along magnetic field lines from a localized source region near the magnetic equator towards the magnetic poles. THEMIS project Electric Field Instrument (EFI) and Search Coil Magnetometer (SCM) measurements were used to determine the spatial scale of the chorus source localization region on the day side of the Earth's outer magnetosphere. We present simultaneous observations of the same chorus elements registered onboard several THEMIS spacecraft in 2007 when all the spacecraft were in the same orbit. Discrete chorus elements were observed at 0.15–0.25 of the local electron gyrofrequency, which is typical for the outer magnetosphere. We evaluated the Poynting flux and wave vector distribution and obtained chorus wave packet quasi-parallel propagation to the local magnetic field. Amplitude and phase correlation data analysis allowed us to estimate the characteristic spatial correlation scale transverse to the local magnetic field to be in the 2800–3200 km range.
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SHAKIROV, Mansur A. "The Poynting Vector and the New Theory of a Transformer. Part 11. Three-Phase Three-Core Transformers without a Neutral Wire." Elektrichestvo 1, no. 1 (2021): 23–34. http://dx.doi.org/10.24160/0013-5380-2021-1-23-34.
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A topological equivalent circuit for a three-phase three-core transformer reflecting the spatial structure of its magnetic system is developed. Owing to this approach, it became possible to represent the magnetic fluxes of the magnetic circuit’s all main sections and the apertures for each of three phases directly in the circuit in the absence of the windings’ neutral wires. The circuit is constructed by stitching together the anatomical circuit models of single-phase transformers obtained in the previous parts with taking into account the relationships between the fluxes at the junctions of the phase zones in iron. Its validity is confirmed by the rigor nature of the physical and mathematical relations for idealized transformers with infinite magnetic permeability of iron and simplified magnetic field patterns, which corresponds to the generally accepted approach with neglecting the magnetization currents. The difference lies in the fact that the developed model takes into account the heterogeneity of magnetization in different parts of the magnetic circuit with allocating more than 30 sections in the iron and apertures. The transition to the model of a real three-core transformer is carried out by adding four nonlinear transverse magnetization branches in each extreme phase zone and eight branches in the central phase zone to the idealized equivalent circuit. It is shown that in cases of winding connections without neutral wires, there is no flux of the Poynting vector in interphase zones in any unbalanced mode. In this case, the problems connected with the occurrence of fluxes exceeding the no-load fluxes under the conditions of symmetric and asymmetric short circuits, as well as the occurrence of buckling fluxes in these modes in the region outside the transformer iron, are solved.
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Korth, H., B. J. Anderson, H. U. Frey, and C. L. Waters. "High-latitude electromagnetic and particle energy flux during an event with sustained strongly northward IMF." Annales Geophysicae 23, no. 4 (June 3, 2005): 1295–310. http://dx.doi.org/10.5194/angeo-23-1295-2005.
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Abstract. We present a case study of a prolonged interval of strongly northward orientation of the interplanetary magnetic field on 16 July 2000, 16:00-19:00 UT to characterize the energy exchange between the magnetosphere and ionosphere for conditions associated with minimum solar wind-magnetosphere coupling. With reconnection occurring tailward of the cusp under northward IMF conditions, the reconnection dynamo should be separated from the viscous dynamo, presumably driven by the Kelvin-Helmholtz (KH) instability. Thus, these conditions are also ideal for evaluating the contribution of a viscous interaction to the coupling process. We derive the two-dimensional distribution of the Poynting vector radial component in the northern sunlit polar ionosphere from magnetic field observations by the constellation of Iridium satellites together with drift meter and magnetometer observations from the Defense Meteorological Satellite Program (DMSP) F13 and F15 satellites. The electromagnetic energy flux is then compared with the particle energy flux obtained from auroral images taken by the far-ultraviolet (FUV) instrument on the Imager for Magnetopause to Aurora Global Exploration (IMAGE) spacecraft. The electromagnetic energy input to the ionosphere of 51 GW calculated from the Iridium/DMSP observations is eight times larger than the 6 GW due to particle precipitation all poleward of 78° MLAT. This result indicates that the energy transport is significant, particularly as it is concentrated in a small region near the magnetic pole, even under conditions traditionally considered to be quiet and is dominated by the electromagnetic flux. We estimate the contributions of the high and mid-latitude dynamos to both the Birkeland currents and electric potentials finding that high-latitude reconnection accounts for 0.8 MA and 45kV while we attribute <0.2MA and ~5kV to an interaction at lower latitudes having the sense of a viscous interaction. Given that these conditions are ideal for the occurrence of the KH instability at the magnetopause and hence the viscous interaction, this result suggests that the viscous interaction is a small contributor to coupling solar wind energy to the magnetosphere-ionosphere system.
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Sergeev, Andrei, and Michael Reizer. "Entropy-based theory of thermomagnetic phenomena." International Journal of Modern Physics B 35, no. 18 (July 14, 2021): 2150190. http://dx.doi.org/10.1142/s0217979221501903.
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We show that in the linear response approximation only entropy provides coupling between thermal and electric phenomena. The dissipationless quantum currents — magnetization, superconducting, persistent and topological edge currents — do not produce and transfer entropy and may be excluded from final formulas for thermomagnetic coefficients. The magnetization energy flux, [Formula: see text], in crossed electric and magnetic fields strongly modifies the Poynting vector in magnetic materials and metamaterials, but do not contribute to the heat current. Calculating entropy fluxes of fluctuating Cooper pairs in pure and disordered superconductors, we obtained the fluctuation Nernst coefficient proportional to [Formula: see text] ([Formula: see text] is the Fermi energy). We also introduce the thermomagnetic entropy per unit charge and derive the Nernst coefficient proportional to the difference of the thermoelectric and thermomagnetic entropies. This explains the Sondheimer cancellation and high sensitivity of thermomagnetic phenomena to correlations. In 2D superconductors, the transport entropy transferred by a vortex moving through the background formed by vortex–antivortex pairs is the configuration entropy of [Formula: see text], which strongly exceeds the intrinsic entropy of vortex core. Beyond the linear response, the nonentropic forces can lead to phenomena unexpected from thermodynamics, such as vortex attraction to the moving hot spot. Quantum currents do not transfer entropy and may be used as ideal connectors to quantum nanodetectors.
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Agapitov, O., V. Krasnoselskikh, Yu Zaliznyak, V. Angelopoulos, O. Le Contel, and G. Rolland. "Observations and modeling of forward and reflected chorus waves captured by THEMIS." Annales Geophysicae 29, no. 3 (March 11, 2011): 541–50. http://dx.doi.org/10.5194/angeo-29-541-2011.
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Abstract. Discrete ELF/VLF chorus emissions are the most intense electromagnetic plasma waves observed in the radiation belts of the Earth's magnetosphere. Chorus emissions, whistler-mode wave packets propagating roughly along magnetic field lines from a well-localized source in the vicinity of the magnetic equator to polar regions, can be reflected at low altitudes. After reflection, wave packets can return to the equatorial plane region. Understanding of whistler wave propagation and reflection is critical to a correct description of wave-particle interaction in the radiation belts. We focus on properties of reflected chorus emissions observed by the THEMIS (Time History of Events and Macroscale Interactions During Substorms) spacecraft Search Coil Magnetometer (SCM) and Electric Field Instrument (EFI) at ELF/VLF frequencies up to 4 kHz at L≥8. We determine the direction of the Poynting flux and wave vector distribution for forward and reflected chorus waves. Although both types of chorus waves were detected near the magnetic equator and have similar, discrete structure and rising tones, reflected waves are attenuated by a factor of 10–30 and have 10% higher frequency than concurrently-observed forward waves. Modeling of wave propagation and reflection using geometrical optics ray-tracing allowed us to determine the chorus source region location and explain observed propagation characteristics. We find that reflected wave attenuation at a certain spatial region is caused by divergence of the ray paths of these non-ducted emissions, and that the frequency shift is caused by generation of the reflected waves at lower L-shells where the local equatorial gyrofrequency is larger.
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Maynard, N. C., D. M. Ober, W. J. Burke, J. D. Scudder, M. Lester, M. Dunlop, J. A. Wild, et al. "Polar, Cluster and SuperDARN evidence for high-latitude merging during southward IMF: temporal/spatial evolution." Annales Geophysicae 21, no. 12 (December 31, 2003): 2233–58. http://dx.doi.org/10.5194/angeo-21-2233-2003.
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Abstract. Magnetic merging on the dayside magnetopause often occurs at high latitudes. Polar measured fluxes of accelerated ions and wave Poynting vectors while skimming the subsolar magnetopause. The measurements indicate that their source was located to the north of the spacecraft, well removed from expected component merging sites. This represents the first use of wave Poynting flux as a merging discriminator at the magnetopause. We argue that wave Poynting vectors, like accelerated particle fluxes and the Walén tests, are necessary, but not sufficient, conditions for identifying merging events. The Polar data are complemented with nearly simultaneous measurements from Cluster in the northern cusp, with correlated observations from the Super-DARN radar, to show that the locations and rates of merging vary. Magnetohydrodynamic (MHD) simulations are used to place the measurements into a global context. The MHD simulations confirm the existence of a high-latitude merging site and suggest that Polar and SuperDARN observed effects are attributable to both exhaust regions of a temporally varying X-line. A survey of 13 merging events places the location at high latitudes whenever the interplanetary magnetic field (IMF) clock angle is less than ~150°. While inferred high-latitude merging sites favor the antiparallel merging hypothesis, our data alone cannot exclude the possible existence of a guide field. Merging can even move away from equatorial latitudes when the IMF has a strong southward component. MHD simulations suggest that this happens when the dipole ilt angle increases or when IMF BX increases the effective dipole tilt.Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; magnetospheric configuration and dynamics; solar wind-magnetosphere interactions)
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Li, Wen, J. Bortnik, R. M. Thorne, C. M. Cully, L. Chen, V. Angelopoulos, Y. Nishimura, J. B. Tao, J. W. Bonnell, and O. LeContel. "Characteristics of the Poynting flux and wave normal vectors of whistler-mode waves observed on THEMIS." Journal of Geophysical Research: Space Physics 118, no. 4 (April 2013): 1461–71. http://dx.doi.org/10.1002/jgra.50176.
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