Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A. [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS—University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2014-10-15
In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
Experimental characterization of nonlinear processes of whistler branch waves
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Ganguli, G.; Rudakov, L.
2016-05-01
Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.
Weak Turbulence in the Magnetosphere: Formation of Whistler Wave Cavity by Nonlinear Scattering
Crabtree, C; Ganguli, G; Mithaiwala, M; Galinsky, V; Shevchenko, V
2011-01-01
We consider the weak turbulence of whistler waves in the in low-\\beta\\ inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminished linear damping and enhanced ability to pitch-angle scatter trapped electrons. In addition, a portion of the scattered wave packets can be reflected near the ionosphere back into the magnetosphere. Through multiple nonlinear scatterings and ionospheric reflections a long-lived wave cavity containing turbulent whistler waves can be formed with the appropriate properties to efficiently pitch-angle scatter trapped e...
Nonlinear generation of whistler waves by an ion beam
Akimoto, K.; Winske, D.
1989-01-01
An electromagnetic hybrid code is used to simulate a new mechanism for whistler wave generation by an ion beam. First, a field-aligned ion beam becomes unstable to the electromagnetic ion/ion right-hand resonant instability which generates large amplitude MHD-like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the electron/whistler instability are significantly enhanced, and whistlers start to grow above the noise level. At the same time, because of the reduced parallel drift speed of the ion beam, the frequencies of the whistlers are also downshifted. Full simulations were performed to isolate and separately investigate the electron/ion whistler instability. The results are in agreement with the assumption of fluid electrons in the hybrid simulations and with the linear theory of the instability.
Stagnation of electron flow by a nonlinearly generated whistler wave
Taguchi, Toshihiro; Mima, Kunioki
2016-01-01
Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel propagating whistler that stops the beam. In this letter, we will show the phenomena in detail and explain the mechanism of whistler mediated beam stagnation.
Rapid decay of nonlinear whistler waves in two dimensions: Full particle simulation
Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro
2017-05-01
The decay of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave is investigated by utilizing a two-dimensional (2D) fully relativistic electromagnetic particle-in-cell code. The simulation is performed under a low-beta condition in which the plasma pressure is much lower than the magnetic pressure. It has been shown that the nonlinear (large-amplitude) parent whistler wave decays through the parametric instability in a one-dimensional (1D) system. The present study shows that there is another channel for the decay of the parent whistler wave in 2D, which is much faster than in the timescale of the parametric decay in 1D. The parent whistler wave decays into two sideband daughter whistlers propagating obliquely with respect to the ambient magnetic field with a frequency close to the parent wave and two quasi-perpendicular electromagnetic modes with a frequency close to zero via a 2D decay instability. The two sideband daughter oblique whistlers also enhance a nonlinear longitudinal electrostatic wave via a three-wave interaction as a secondary process.
Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
Energy Technology Data Exchange (ETDEWEB)
Saito, Shinji, E-mail: saito@stelab.nagoya-u.ac.jp [Graduate School of Science, Nagoya University, Nagoya (Japan); Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan); Nariyuki, Yasuhiro, E-mail: nariyuki@edu.u-toyama.ac.jp [Faculty of Human Development, University of Toyama, Toyama (Japan); Umeda, Takayuki, E-mail: umeda@stelab.nagoya-u.ac.jp [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan)
2015-07-15
A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.
Nonlinear Dynamics of Kinetic Alfvén and Whistler Waves in the Solar Wind
Rai, Rajesh Kumar; Sharma, Swati; Sharma, R. P.
2017-03-01
In this article we investigate the nonlinear dynamics of 3D kinetic Alfvén waves (KAWs) and quasi-transverse weak whistler waves in a magnetized plasma. We have studied the problem numerically to examine the transient evolution of localized structures of 3D KAWs and whistler waves. The nonlinearity arises as a result of ponderomotive effects associated with 3D KAWs; consequently, the background density modifies. The weak whistler waves propagating in this modified density are localized and amplified. To improve our insight into the basic physics behind the formation of these localized structures, we have also solved the system semi-analytically. The power spectra show a Kolmogorov scaling (with a power of -5/3) in the inertial range that lies above the ion gyroradius. Below this scale, dispersive effects start to appear, and the power spectrum follows a steeper scaling (-2 to -4). Our results show the important role that KAWs and whistler waves play in the energy cascading from larger to smaller scales. The results are consistent with the solar wind observations by the Cluster spacecraft.
Electron acceleration during the decay of nonlinear Whistler waves in low-beta electron-ion plasma
Energy Technology Data Exchange (ETDEWEB)
Umeda, Takayuki; Saito, Shinji [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya City, Aichi 464-8601 (Japan); Nariyuki, Yasuhiro, E-mail: umeda@stelab.nagoya-u.ac.jp, E-mail: saito@stelab.nagoya-u.ac.jp, E-mail: nariyuki@edu.u-toyama.ac.jp [Faculty of Human Development, University of Toyama, Toyama City, Toyama 930-8555 (Japan)
2014-10-10
Relativistic electron acceleration through dissipation of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave in low-beta plasma is investigated by utilizing a one-dimensional fully relativistic electromagnetic particle-in-cell code. The nonlinear (large-amplitude) parent whistler wave decays through the parametric instability which enhances electrostatic ion acoustic waves and electromagnetic whistler waves. These waves satisfy the condition of three-wave coupling. Through the decay instability, the energy of electron bulk velocity supporting the parent wave is converted to the thermal energy perpendicular to the background magnetic field. Increase of the perpendicular temperature triggers the electron temperature anisotropy instability which generates broadband whistler waves and heats electrons in the parallel direction. The broadband whistler waves are inverse-cascaded during the relaxation of the electron temperature anisotropy. In lower-beta conditions, electrons with a pitch angle of about 90° are successively accelerated by inverse-cascaded whistler waves, and selected electrons are accelerated to over a Lorentz factor of 10. The result implies that the nonlinear dissipation of a finite-amplitude and short-wavelength whistler wave plays an important role in producing relativistic nonthermal electrons over a few MeV especially at lower beta plasmas.
Agapitov, Oleksiy; Drake, James; Mozer, Forrest
2016-04-01
Huge numbers of different nonlinear structures (double layers, electron holes, non-linear whistlers, etc. referred to as Time Domain Structures - TDS) have been observed by the electric field experiment on board the Van Allen Probes. A large part of the observed non-linear structures are associated with whistler waves and some of them can be directly driven by whistlers. The parameters favorable for the generation of TDS were studied experimentally as well as making use of 2-D particle-in-cell (PIC) simulations for the system with inhomogeneous magnetic field. It is shown that an outward propagating front of whistlers and hot electrons amplifies oblique whistlers which collapse into regions of intense parallel electric field with properties consistent with recent observations of TDS from the Van Allen Probe satellites. Oblique whistlers seed the parallel electric fields that are driven by the beams. The resulting parallel electric fields trap and heat the precipitating electrons. These electrons drive spikes of intense parallel electric field with characteristics similar to the TDSs seen in the VAP data. The decoupling of the whistler wave and the nonlinear electrostatic component is shown in PIC simulation in the inhomogeneous magnetic field system. These effects are observed by the Van Allen Probes in the radiation belts. The precipitating hot electrons propagate away from the source region in intense bunches rather than as a smooth flux.
Goyal, R.; Sharma, R. P.; Kumar, S.
2017-01-01
A model is proposed to study the dynamics of high-amplitude quasi-electrostatic whistler waves propagating near resonance cone angle and their interaction with low-frequency kinetic Alfvén waves (KAWs) in Earth's radiation belts. The wave dynamics clearly indicates the whistlers having quasi-electrostatic character when propagating close to resonance cone angle. A high-amplitude whistler wave packet is obtained using the present analysis which has also been observed by S/WAVES (STEREO/WAVES) instrument onboard STEREO (Solar Terrestrial Relations Observatory). A numerical simulation technique has been employed to study the localization of quasi-electrostatic whistler waves in radiation belts. The ponderomotive force of pump quasi-electrostatic whistlers (high frequency) is used to excite low-frequency waves (KAWs). The turbulent spectrum obtained using the analysis suggests the presence of quasi-electrostatic whistlers and density fluctuations associated with KAW in radiation belts plasma. The wave localization and steeper spectra could be responsible for particle energization or heating in radiation belts.
Camporeale, Enrico; Zimbardo, G.
2015-01-01
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in ...
Self-focusing of whistler waves
Karpman, V. I.; Kaufman, R. N.; Shagalov, A. G.
1992-01-01
The theory of axially symmetric self-focusing of whistler waves, based on the full system of Maxwell equations, is developed. The plasma is described by the magnetohydrodynamic equations including the ponderomotive force from RF field. The nonlinear Schrodinger equations (NSE) for arbitrary azimuthal modes of whistler waves are derived. It is shown that they differ from the NSE for a scalar field; this is connected with an intrinsic angular momentum due to the rotating polarization of whistlers. It is shown that the self-focusing, as described by the NSE, differs in its final stage from the results following the full set of Maxwell equations. The latter gives defocusing after sufficient narrowing of the initial wave beam, due to transformation of the trapped wave into a nontrapped branch which is not contained in the NSE description. The oscillatory character of the defocusing is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Camporeale, Enrico, E-mail: e.camporeale@cwi.nl [Center for Mathematics and Computer Science (CWI), 1098 XG Amsterdam (Netherlands); Zimbardo, Gaetano [Department of Physics, University of Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Rende (Italy)
2015-09-15
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.
Camporeale, Enrico
2014-01-01
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles, and comparing with test-particles simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates. We discuss how the saturation is related to the fact that the domain in which the particles' pitch angle diffuse is bounded, and to the well-known problem of $90^\\circ$ diffusion barrier.
National Research Council Canada - National Science Library
Wilder, F. D; Ergun, R. E; Goodrich, K. A; Goldman, M. V; Newman, D. L; Malaspina, D. M; Jaynes, A. N; Schwartz, S. J; Trattner, K. J; Burch, J. L; Argall, M. R; Torbert, R. B; Lindqvist, P.‐A; Marklund, G; Le Contel, O; Mirioni, L; Khotyaintsev, Yu. V; Strangeway, R. J; Russell, C. T; Pollock, C. J; Giles, B. L; Plaschke, F; Magnes, W; Eriksson, S; Stawarz, J. E; Sturner, A. P; Holmes, J. C
2016-01-01
.... Bipolar parallel electric fields interpreted as electrostatic solitary waves (ESW) are observed intermittently and appear to be in phase with the parallel component of the whistler oscillations...
Potential role of kinetic Alfvén waves and whistler waves in solar wind plasmas
Nandal, P.; Yadav, N.; Sharma, R. P.; Goldstein, M. L.
2016-07-01
Spacecraft observations indicate the signatures of highly oblique kinetic Alfvén waves (KAWs) and whistler waves in the solar wind plasma. In the present work, we explore the possible role of KAWs and whistler waves in the observed solar wind magnetic turbulent spectrum. The nonlinear spatial evolution of KAW is studied including the effects of the ponderomotive force which results in intense localized structures due to the background density modification. Weak quasi-transverse whistler wave propagating through these localized structures also gets localized in the form of small-scale localized structures. We present numerically calculated magnetic power spectra for both KAW as well as for whistler wave. Our obtained results demonstrate the important role that KAWs and whistler waves play in the energy cascading from larger to smaller scales. The relevance of these results to recent spacecraft observations is also pointed out.
Localization and implication of oblique whistler wave in the magnetopause region
Nandal, P.; Yadav, N.; Sharma, R. P.
2016-04-01
Nonlinear interaction between highly oblique whistler wave and ion acoustic wave pertinent to magnetopause has been investigated. The density perturbation in whistler wave is supposed to be originated due to the presence of ion acoustic wave in the background. The ponderomotive force components arising due to the high amplitude pump wave, viz., whistler wave are constituted in the nonlinear dynamics of low frequency ion acoustic wave. The coupled nonlinear dynamical equations are then modelled in the form of modified nonlinear Schrödinger equation by considering adiabatic response of low frequency ion acoustic wave. The numerical simulation of this coupled nonlinear equation is performed to study the temporal evolution of nonlinear whistler wave. The obtained simulation results show that the temporal evolution also leads to the cascade of broadband turbulence spectrum at smaller wavelengths. The relevance of the obtained results with the observations of THEMIS spacecraft in the magnetopause region has been pointed out.
Parametric excitation of whistler waves by HF heater
Kuo, S. P.; Lee, M. C.
1989-01-01
Possible generation of whistler waves by Tromso HF heater is investigated. It is shown that the HF heater wave can parametrically decay into a whistler wave and a Langmuir wave. Since whistler waves may have a broad range of frequency, the simultaneously excited Langmuir waves can have a much broader frequency bandwidth than those excited by the parametric decay instability.
Camporeale, E.; Zimbardo, G.
2014-01-01
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles, and comparing with test-particles simulations we emphasi
Camporeale, E.; Zimbardo, G.
2015-01-01
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles, and comparing with test-particles simulations we emphasi
Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner
Kaya, N.; Matsumoto, H.; Tsurutani, B. T.
1989-01-01
Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.
Agapitov, Oleksiy; Artemyev, Anton; Mourenas, Didier; Mozer, Forrest; Krasnoselskikh, Vladimir
2016-04-01
Simultaneous observations of electron velocity distributions and chorus waves by the Van Allen Probe B are analyzed to identify long-lasting (more than 6 h) signatures of electron Landau resonant interactions with oblique chorus waves in the outer radiation belt. Such Landau resonant interactions result in the trapping of ˜1-10 keV electrons and their acceleration up to 100-300 keV. This kind of process becomes important for oblique whistler mode waves having a significant electric field component along the background magnetic field. In the inhomogeneous geomagnetic field, such resonant interactions then lead to the formation of a plateau in the parallel (with respect to the geomagnetic field) velocity distribution due to trapping of electrons into the wave effective potential. We demonstrate that the electron energy corresponding to the observed plateau remains in very good agreement with the energy required for Landau resonant interaction with the simultaneously measured oblique chorus waves over 6 h and a wide range of L shells (from 4 to 6) in the outer belt. The efficient parallel acceleration modifies electron pitch angle distributions at energies ˜50-200 keV, allowing us to distinguish the energized population. The observed energy range and the density of accelerated electrons are in reasonable agreement with test particle numerical simulations.
Wilder, F. D.; Ergun, R. E.; Goodrich, K. A.; Goldman, M. V.; Newman, D. L.; Malaspina, D. M.; Jaynes, A. N.; Schwartz, S. J.; Trattner, K. J.; Burch, J. L.; Argall, M. R.; Torbert, R. B.; Lindqvist, P.-A.; Marklund, G.; Le Contel, O.; Mirioni, L.; Khotyaintsev, Yu. V.; Strangeway, R. J.; Russell, C. T.; Pollock, C. J.; Giles, B. L.; Plaschke, F.; Magnes, W.; Eriksson, S.; Stawarz, J. E.; Sturner, A. P.; Holmes, J. C.
2016-06-01
We show observations from the Magnetospheric Multiscale (MMS) mission of whistler mode waves in the Earth's low-latitude boundary layer (LLBL) during a magnetic reconnection event. The waves propagated obliquely to the magnetic field toward the X line and were confined to the edge of a southward jet in the LLBL. Bipolar parallel electric fields interpreted as electrostatic solitary waves (ESW) are observed intermittently and appear to be in phase with the parallel component of the whistler oscillations. The polarity of the ESWs suggests that if they propagate with the waves, they are electron enhancements as opposed to electron holes. The reduced electron distribution shows a shoulder in the distribution for parallel velocities between 17,000 and 22,000 km/s, which persisted during the interval when ESWs were observed, and is near the phase velocity of the whistlers. This shoulder can drive Langmuir waves, which were observed in the high-frequency parallel electric field data.
Whistler mode waves in the Jovian magnetosheath
Lin, Naiguo; Kellogg, P. J.; Thiessen, J. P.; Lengyel-Frey, D.; Tsurutani, B. T.; Phillips, J. L.
1994-01-01
During the Ulysses flyby of Jupiter in February 1992, the spacecraft traversed the Jovian magnetosheath for a few hours during the inbound pass and for aa few days during the outbound pass. Burstlike electomagnetic waves at frequencies of approximately 0.1-0.4 of the local electron cyclotron frequency have been observed by the Unified Radio and Plasma Wave (URAP) experiement. The waves were more often observed in the regions which were probably the outer or the middle magnetosheath, especially near the bow shock, and rarely seen in the magnetosphere/magnetosheath boundary layer. The propagation angles of the waves are estimated by comparing the measurements of the wave electric and magnetic fields in the spacecraft spin plane with the corresponding values calculated using the cold plasma dispersion relation under local field and plasma conditions. It is found that the waves propagate obliquely with wave angles between approximately 30 deg and 50 deg. These waves are likely to be the whistler mode waves which are excited by suprathermal electrons with a few hundred eV and a slight anisotropy (T(sub perp)/T(sub parallel) approximately 1.1-1.5). They are probably similar in nature to the lion roars observed in the Earth's magnetosheath. Signature of coupling between the mirror and the whistler mode have also been observed. The plasma conditions which favor the excitation of the whistler mode instability during the wave events exists as observed by the plasma experiement of Ulysses.
Whistler Waves Associated with Weak Interplanetary Shocks
Velez, J. C. Ramirez; Blanco-Cano, X.; Aguilar-Rodriguez, E.; Russell, C. T.; Kajdic, P.; Jian,, L. K.; Luhmann, J. G.
2012-01-01
We analyze the properties of 98 weak interplanetary shocks measured by the dual STEREO spacecraft over approximately 3 years during the past solar minimum. We study the occurrence of whistler waves associated with these shocks, which on average are high beta shocks (0.2 whistler waves can extend up to 100,000 km in the upstream region but in most cases (88%) are contained in a distance within 30,000 km from the shock. This corresponds to a larger region with upstream whistlers associated with IP shocks than previously reported in the literature. The maximum amplitudes of the waves are observed next to the shock interface, and they decrease as the distance to the shock increases. In most cases the wave propagation direction becomes more aligned with the magnetic field as the distance to the shock increases. These two facts suggest that most of the waves in the upstream region are Landau damping as they move away from the shock. From the analysis we also conclude that it is likely that the generation mechanism of the upstream whistler waves is taking place at the shock interface. In the downstream region, the waves are irregularly polarized, and the fluctuations are very compressive; that is, the compressive component of the wave clearly dominates over the transverse one. The majority of waves in the downstream region (95%) propagate at oblique angles with respect to the ambient magnetic field (>60 deg.). The wave propagation with respect to the shock-normal direction has no preferred direction and varies similarly to the upstream case. It is possible that downstream fluctuations are generated by ion relaxation as suggested in previous hybrid simulation shocks.
Exitation of Whistler Waves by a Helical Wave Structure
DEFF Research Database (Denmark)
Balmashnov, A. A.; Lynov, Jens-Peter; Michelsen, Poul
1981-01-01
The excitation of whistler waves in a radial inhomogeneous plasma is investigated experimentally, using a slow-wave structure consisting of a helix of variable length surrounding the plasma column. The excited waves were observed to have a wave-vector parallel to the external magnetic field....... The possibility of exciting the waves in different radial regions is demonstrated....
Upconversion of whistler waves by gyrating ion beams in a plasma
Indian Academy of Sciences (India)
Harsha Jalori; Sunil K Singh; A K Gwal
2004-09-01
A gyrating ion beam, with a ring-shaped distribution in velocity, supports negative energy beam modes near the harmonics of beam gyro-frequency. An investigation of the non-linear interaction of high-frequency whistler waves with the negative energy beam cyclotron mode is made. A non-linear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion-beam frequency upconverts the whistler waves separated by harmonics of beam gyro-frequency. The expression for the growth rate of whistler mode waves has been derived. In Case 1, a high-amplitude whistler wave decays into two lower frequency waves, called a low-frequency mode and a side band of frequency lower than that of pump wave. In Case 2 a high-amplitude whistler wave decays into two lower frequency daughter waves, called the low-frequency mode and whistler waves. Generation mechanism of these waves has application in space and laboratory plasmas.
Proton beam generation of oblique whistler waves
Wong, H. K.; Goldstein, M. L.
1988-01-01
It is known that ion beams are capable of generating whistler waves that propagate parallel to the mean magnetic field. Such waves may have been observed both upstream of the earth's bow shock and in the vicinity of comets. Previous analyses are extended to include propagation oblique to the mean magnetic field. The instability is generated by the perpendicular component of free energy in the ions, which can arise either via a temperature anisotropy or via a gyrating distribution. In the former case, the generation of whistler waves is confined to a fairly narrow cone of propagation directions centered about parallel propagation; in the latter case, the maximum growth of the instability can occur at fairly large obliquities (theta equal to about 50 deg).
Whistler Mode Waves in Collisionless Magnetic Reconnection
Institute of Scientific and Technical Information of China (English)
GUO Jun; LU Quan-Ming; WANG Shui; WANG Yu-Ming; DOU Xian-Kang
2004-01-01
A 21/2-dimensional electromagnetic particle-in-cell (PIC) simulation code is used to investigate the wave phenomena in the plasma sheet of collisionless magnetic reconnection. The results show that these waves have the following characteristics: they are right-hand circularity polarized, with propagation direction nearly parallel to local magnetic field, and frequency between 0.07 and 0.17 times of local electron cyclotron frequency. Therefore we conclude that such waves are Whistler waves, and their possible excitation mechanisms are also discussed.
Coupling between whistler waves and slow-mode solitary waves
Tenerani, Anna; Pegoraro, Francesco; Contel, Olivier Le
2012-01-01
The interplay between electron-scale and ion-scale phenomena is of general interest for both laboratory and space plasma physics. In this paper we investigate the linear coupling between whistler waves and slow magnetosonic solitons through two-fluid numerical simulations. Whistler waves can be trapped in the presence of inhomogeneous external fields such as a density hump or hole where they can propagate for times much longer than their characteristic time scale, as shown by laboratory experiments and space measurements. Space measurements have detected whistler waves also in correspondence to magnetic holes, i.e., to density humps with magnetic field minima extending on ion-scales. This raises the interesting question of how ion-scale structures can couple to whistler waves. Slow magnetosonic solitons share some of the main features of a magnetic hole. Using the ducting properties of an inhomogeneous plasma as a guide, we present a numerical study of whistler waves that are trapped and transported inside pr...
Two types of whistler waves in the hall reconnection region
Huang, S. Y.; Fu, H. S.; Yuan, Z. G.; Vaivads, A.; Khotyaintsev, Y. V.; Retino, A.; Zhou, M.; Graham, D. B.; Fujimoto, K.; Sahraoui, F.; Deng, X. H.; Ni, B.; Pang, Y.; Fu, S.; Wang, D. D.; Zhou, X.
2016-07-01
Whistler waves are believed to play an important role during magnetic reconnection. Here we report the near-simultaneous occurrence of two types of the whistler-mode waves in the magnetotail Hall reconnection region. The first type is observed in the magnetic pileup region of downstream and propagates away to downstream along the field lines and is possibly generated by the electron temperature anisotropy at the magnetic equator. The second type, propagating toward the X line, is found around the separatrix region and probably is generated by the electron beam-driven whistler instability or Čerenkov emission from electron phase-space holes. These observations of two different types of whistler waves are consistent with recent kinetic simulations and suggest that the observed whistler waves are a consequence of magnetic reconnection.
Enhanced Plasma Confinement in a Magnetic Well by Whistler Waves
DEFF Research Database (Denmark)
Balmashnov, A. A.; Juul Rasmussen, Jens
1981-01-01
The propagation of whistler waves in a magnetic field of mirror configuration is investigated experimentally. The strong interaction between waves and particles at the electron-cyclotron resonance leads to enhanced confinement in the magnetic well.......The propagation of whistler waves in a magnetic field of mirror configuration is investigated experimentally. The strong interaction between waves and particles at the electron-cyclotron resonance leads to enhanced confinement in the magnetic well....
Bursty emission of whistler waves in association with plasmoid collision
Directory of Open Access Journals (Sweden)
K. Fujimoto
2017-07-01
Full Text Available A new mechanism to generate whistler waves in the course of collisionless magnetic reconnection is proposed. It is found that intense whistler emissions occur in association with plasmoid collisions. The key processes are strong perpendicular heating of the electrons through a secondary magnetic reconnection during plasmoid collision and the subsequent compression of the ambient magnetic field, leading to whistler instability due to the electron temperature anisotropy. The emissions have a bursty nature, completing in a short time within the ion timescales, as has often been observed in the Earth's magnetosphere. The whistler waves can accelerate the electrons in the parallel direction, contributing to the generation of high-energy electrons. The present study suggests that the bursty emission of whistler waves could be an indicator of plasmoid collisions and the associated particle energization during collisionless magnetic reconnection.
Whistler Wave Energy Flow in the Plasmasphere
Kletzing, Craig; Santolik, Ondrej; Kurth, William; Hospodarsky, George; Christopher, Ivar; Bounds, Scott
2016-07-01
The measured wave properties of plasmaspheric hiss are important to constrain models of the generation of hiss as well as its propagation and amplification. For example, the generation mechanism for plasmaspheric hiss has been suggested to come from one of three possible mechanisms: 1) local generation and amplification, 2) whistlers from lightning, and 3) chorus emissions which have refracted into the plasmasphere. The latter two mechanisms are external sources which produce an incoherent hiss signature as the original waves mix in a stochastic manner, propagating in both directions along the background magnetic field. In contrast, local generation of plasmaspheric hiss within the plasmasphere should produce a signature of waves propagating away from the source region. For all three mechanisms scattering of energetic particles into the loss cone transfers some energy from the particles to the waves. By examining the statistical characteristics of the Poynting flux of plasmaspheric hiss, we can determine the properties of wave energy flow in the plasmasphere. We report on the statistics of observations from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) Waves instrument on the Van Allen Probes for periods when the spacecraft is inside the plasmasphere. We find that the Poynting flux associated with plasmaspheric hiss has distinct and unexpected radial structure which shows that there can be significant energy flow towards the magnetic equator. We show the properties of this electromagnetic energy flow as a function of position and frequency.
An analysis of whistler waves at interplanetary shocks
Lengyel-Frey, D.; Farrell, W. M.; Stone, R. G.; Balogh, A.; Forsyth, R.
1994-01-01
We present an analysis of whistler wave magnetic and electric field amplitude ratios from which we compute wave propagation angles and energies of electrons in resonance with the waves. To do this analysis, we compute the theoretical dependence of ratios of wave components on the whistler wave propagation angle Theta for various combinations of orthogonal wave components. Ratios of wave components that would be observed by a spinning spacecraft are determined, and the effects of arbitrary inclinations of the spacecraft to the ambient magnetic field and to the whistler wave vector are studied. This analysis clearly demonstrates that B/E, the ratio of magnetic to electric field amplitudes, cannot be assumed to be the wave index of refraction, contrary to assumptions of some earlier studies. Therefore previous interpretations of whistler wave observations based on this assumption must be reinvestigated. B/E ratios derived using three orthogonal wave components can be used to unambiguously determine Theta. Using spin plane observations alone, a significant uncertainty occurs in the determination of Theta. Nevertheless, for whistler waves observed downstream of several interplanetary shocks by the Ulysses plasma wave experiment we find that Theta is highly oblique. We suggest that the analysis of wave amplitude ratios used in conjunction with traditional stability analyses provide a promising tool for determining which particle distributions and resonances are likely to be dominant contributors to wave growth.
Transport of time-varying plasma currents by whistler wave packets
Stenzel, R. L.; Urrutia, J. M.; Rousculp, C.
1992-01-01
The relationship between pulsed currents and electromagnetic waves is examined in a regime characterized by electron MHD. Pulsed currents are generated by (1) collection/emission of charged particles by/from biased electrodes and (2) induction of currents by time-varying and moving magnetic fields. Pulsed currents are observed to propagate at the speed of whistler wave packets. Their field structure forms ropelike configurations which are electromagnetically force-free. Moving sources induce 'eddy' currents which excite waves and form Cerenkov-like whistler 'wings'. The radiation patterns of moving magnetic antennas and electrodynamic tethers are investigated. Nonlinear effects of large-amplitude, antenna-launched whistler pulses are observed. These involve a new modulational instability in which a channel of high conductivity which permits the wave/currents to penetrate deeply into a collisional plasma is formed.
Pitch angle scattering of energetic particles by oblique whistler waves
Inan, U. S.; Bell, T. F.
1991-01-01
First order cyclotron or Landau resonant pitch angle scattering of electrons by oblique whistler waves propagating at large angles to the ambient field are found to be at least as large as that due to parallel propagating waves. Commonly observed precipitation of more than 40 keV electrons in association with ducted whistlers may thus be accompanied by substantial fluxes of lower energy (10 eV-40 keV) electrons precipitated by the nonducted components.
Electron Whistler Mode Waves Associated with Collisionless Magnetic Reconnection
Institute of Scientific and Technical Information of China (English)
GUO Jun; YU Bin; GUO Guang-Hai; ZHAO Bo
2011-01-01
@@ The results of particle-in-cell (PIC) simulations are presented on the evolution of the electron whistler waves during the collisionless magnetic reconnection.The simulation results show that the electron whistler waves with frequency higher than the lower hybrid frequency are found to occur in the electrons outflow region.Moreover, the present results indicate that these electron whistler waves with high-frequency in the region greater than an ion inertial scale of the x-line are irrelevant to the fast reconnection, but are generated as a result of the reconnection processes.%The results of particle-in-cell (PIC) simulations are presented on the evolution of the electron whistler waves during the collisionless magnetic reconnection. The simulation results show that the electron whistler waves with frequency higher than the lower hybrid frequency are found to occur in the electrons outflow region. Moreover,the present results indicate that these electron whistler waves with high-frequency in the region greater than an ion inertial scale of the x-line are irrelevant to the fast reconnection, but are generated as a result of the reconnection processes.
Proton beam generation of whistler waves in the earth's foreshock
Wong, H. K.; Goldstein, M. L.
1987-01-01
It is shown that proton beams, often observed upstream of the earth's bow shock and associated with the generation of low-frequency hydromagnetic fluctuations, are also capable of generating whistler waves. The waves can be excited by an instability driven by two-temperature streaming Maxwellian proton distributions which have T (perpendicular)/T(parallel) much greater than 1. It can also be excited by gyrating proton beam distributions. These distributions generate whistler waves with frequencies ranging from 10 to 100 times the proton cyclotron frequency (in the solar wind reference frame) and provide another mechanism for generating the '1-Hz' waves often seen in the earth's foreshock.
Electron acceleration by Landau resonance with whistler mode wave packets
Gurnett, D. A.; Reinleitner, L. A.
1983-01-01
Recent observations of electrostatic waves associated with whistler mode chorus emissions provide evidence that electrons are being trapped by Landau resonance interactions with the chorus. In this paper, the trapping, acceleration and escape of electrons in Landau resonance with a whistler mode wave packet are discussed. It is shown that acceleration can occur by both inhomogeneous and dispersive effects. The maximum energy gained is controlled by the points where trapping and escape occur. Large energy changes are possible if the frequency of the wave packet or the magnetic field strength increase between the trapping and escape points. Various trapping and escape mechanisms are discussed.
Excitation of Chirping Whistler Waves in a Laboratory Plasma.
Van Compernolle, B; An, X; Bortnik, J; Thorne, R M; Pribyl, P; Gekelman, W
2015-06-19
Whistler mode chorus emissions with a characteristic frequency chirp are important magnetospheric waves, responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Here, we report on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced using a beam of energetic electrons launched into a cold plasma. Frequency chirps are only observed for a narrow range of plasma and beam parameters, and show a strong dependence on beam density, plasma density, and magnetic field gradient. Broadband whistler waves similar to magnetospheric hiss are also observed, and the parameter ranges for each emission are quantified.
Excitation of Chirping Whistler Waves in a Laboratory Plasma
Van Compernolle, B.; An, X.; Bortnik, J.; Thorne, R. M.; Gekelman, W. N.; Pribyl, P.
2015-12-01
Whistler mode chorus emissions with a characteristic frequency chirp are an important magnetospheric wave, responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Here, we report on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced using a beam of energetic electrons launched into a cold plasma. Frequency chirps are only observed for a narrow range of plasma and beam parameters, and show a strong dependence on beam density, plasma density and magnetic field gradient. Broadband whistler waves similar to magnetospheric hiss are also observed, and the parameter ranges for each emission are quantified. The research was funded by NSF/DOE Plasma Partnership program by grant DE-SC0010578. Work was done at the Basic Plasma Science Facility (BAPSF) also funded by NSF/DOE.
Kersten, K.; Cattell, C. A.; Breneman, A.; Goetz, K.; Kellogg, P. J.; Wygant, J. R.; Wilson, L. B., III; Blake, J. B.; Looper, M. D.; Roth, I.
2011-01-01
We present multi-satellite observations of large amplitude radiation belt whistler-mode waves and relativistic electron precipitation. On separate occasions during the Wind petal orbits and STEREO phasing orbits, Wind and STEREO recorded intense whistler-mode waves in the outer nightside equatorial radiation belt with peak-to-peak amplitudes exceeding 300 mV/m. During these intervals of intense wave activity, SAMPEX recorded relativistic electron microbursts in near magnetic conjunction with Wind and STEREO. This evidence of microburst precipitation occurring at the same time and at nearly the same magnetic local time and L-shell with a bursty temporal structure similar to that of the observed large amplitude wave packets suggests a causal connection between the two phenomena. Simulation studies corroborate this idea, showing that nonlinear wave.particle interactions may result in rapid energization and scattering on timescales comparable to those of the impulsive relativistic electron precipitation.
Chaotic Motion of Relativistic Electrons Driven by Whistler Waves
Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.
2007-01-01
Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.
Sundkvist, David; Krasnoselskikh, V; Bale, S D; Schwartz, S J; Soucek, J; Mozer, F
2012-01-13
Whistler wave trains are observed in the foot region of high Mach number quasiperpendicular shocks. The waves are oblique with respect to the ambient magnetic field as well as the shock normal. The Poynting flux of the waves is directed upstream in the shock normal frame starting from the ramp of the shock. This suggests that the waves are an integral part of the shock structure with the dispersive shock as the source of the waves. These observations lead to the conclusion that the shock ramp structure of supercritical high Mach number shocks is formed as a balance of dispersion and nonlinearity.
Parametric decay of a parallel propagating monochromatic whistler wave: Particle-in-cell simulations
Ke, Yangguang; Gao, Xinliang; Lu, Quanming; Wang, Shui
2017-01-01
In this paper, by using one-dimensional (1-D) particle-in-cell simulations, we investigate the parametric decay of a parallel propagating monochromatic whistler wave with various wave frequencies and amplitudes. The pump whistler wave can decay into a backscattered daughter whistler wave and an ion acoustic wave, and the decay instability grows more rapidly with the increase of the frequency or amplitude. When the frequency or amplitude is sufficiently large, a multiple decay process may occur, where the daughter whistler wave undergoes a secondary decay into an ion acoustic wave and a forward propagating whistler wave. We also find that during the parametric decay a considerable part of protons can be accelerated along the background magnetic field by the enhanced ion acoustic wave through the Landau resonance. The implication of the parametric decay to the evolution of whistler waves in Earth's magnetosphere is also discussed in the paper.
On the Self-Focusing of Whistler Waves in a Radial Inhomogeneous Plasma
DEFF Research Database (Denmark)
Balmashnov, A. A.
1980-01-01
The process of whistler wave self-focusing is experimentally investigated. It was found that a whistler wave propagating along the plasma column with a density crest excites a longitudinal wave of the same frequency propagating across the external magnetic field. The amplitude modulation...... of the latter wave is accompanied by a density modification, which leads to trapping of the whistler wave in a density trough in the center of the plasma column....
Whistler modes with wave magnetic fields exceeding the ambient field.
Stenzel, R L; Urrutia, J M; Strohmaier, K D
2006-03-10
Whistler-mode wave packets with fields exceeding the ambient dc magnetic field have been excited in a large, high electron-beta plasma. The waves are induced with a loop antenna with dipole moment either along or opposite to the dc field. In the latter case the excited wave packets have the topology of a spheromak but are propagating in the whistler mode along and opposite to the dc magnetic field. Field-reversed configurations with net zero helicity have also been produced. The electron magnetohydrodynamics fields are force free, have wave energy density exceeding the particle energy density, and propagate stably at subelectron thermal velocities through a nearly uniform stationary ion density background.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina
2014-01-01
Particle-in-cell code, EPOCH, is used for studying features of the wave component evident to propagate backwards from the front of the non-gyrotropic, relativistic beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile. According to recent findings presented in Tsiklauri (2011), Schmitz & Tsiklauri (2013) and Pechhacker & Tsiklauri (2012), in a 1.5-dimensional magnetised plasma system, the non-gyrotropic beam generates freely escaping electromagnetic radiation with properties similar to the Type-III solar radio bursts. In this study the backwards propagating wave component evident in the perpendicular components of the elecromagnetic field in such a system is presented for the first time. Background magnetic field strength in the system is varied in order to prove that the backwards propagating wave's frequency, prescribed by the whistler wave dispersion relation, is proportional to the specified magnetic field. Moreover, the identified whistlers are...
Directory of Open Access Journals (Sweden)
K. Sauer
2010-06-01
Full Text Available Isotropic electron beams are considered to explain the excitation of whistler waves which have been observed by the STEREO satellite in the Earth's radiation belt. Aside from their large amplitudes (~240 mV/m, another main signature is the strongly inclined propagation direction relative to the ambient magnetic field. Electron temperature anisotropy with T_{e⊥}>T_{e||}, which preferentially generates parallel propagating whistler waves, can be excluded as a free energy source. The instability arises due to the interaction of the Doppler-shifted cyclotron mode ω=−Ω_{e}+kV_{b}cosθ with the whistler mode in the wave number range of kc/ω_{e}≤1 (θ is the propagation angle with respect to the background magnetic field direction, ω_{e} is the electron plasma frequency and Ω_{e} the electron cyclotron frequency. Fluid and kinetic dispersion analysis have been used to calculate the growth rate of the beam-excited whistlers including the most important parameter dependencies. One is the beam velocity (V_{b} which, for instability, has to be larger than about 2V_{Ae}, where V_{Ae} is the electron Alfvén speed. With increasing V_{Ae} the propagation angle (θ of the fastest growing whistler waves shifts from θ~20° for V_{b}=2V_{Ae} to θ~80° for V_{b}=5V_{Ae}. The growth rate is reduced by finite electron temperatures and disappears if the electron plasma beta (β_{e} exceeds β_{e}~0.2. In addition, Gendrin modes (kc/ω_{e}≈1 are analyzed to determine the conditions under which stationary nonlinear waves (whistler oscillitons can exist. The corresponding spatial wave profiles are calculated using the full nonlinear fluid approach. The results are compared with the STEREO satellite observations.
Propagation of whistler waves driven by fine structured ion beams in the magnetotail
Burinskaya, T.; Schriver, D.; Ashour-Abdalla, M.
1994-01-01
In a previous paper, which examined the propagation of low-frequency whistler waves generated by ion beams in the Earth's plasma sheet boundary layer (PSBL), it was found that whistler waves driven in the PSBL are focused toward the central plasma sheet due to the global magnetotail inhomogeneities; this finding may help explain the observations of magnetic noise bursts in the tail (Burinskaya et al., 1993). In this paper the same phenomenon is examined, but this time a much more realistic model is used for the ion beam in the PSBL. While the PSBL has been modeled as a solid, homogeneous ion beams with a width of one Earth radius, observations and theoretical considerations have shown that PSBL ion beams actually have a decreasing velocity profile toward the plasma sheet and that the density of the beams within the PSBL can vary locally. We consider again the propagation and generation of electromagnetic waves but in the presence of fine structured ion beams in the PSBL. Our results show that whistler waves, generated quasi-parallel to the background magnetic field, can be trapped locally within small spatial regions where the ion beam density is enhanced compared to the density of the adjacent PSBL region. Wave spectra and nonlinear saturation mechanisms are discussed.
Measurements of parallel electron velocity distributions using whistler wave absorption.
Thuecks, D J; Skiff, F; Kletzing, C A
2012-08-01
We describe a diagnostic to measure the parallel electron velocity distribution in a magnetized plasma that is overdense (ω(pe) > ω(ce)). This technique utilizes resonant absorption of whistler waves by electrons with velocities parallel to a background magnetic field. The whistler waves were launched and received by a pair of dipole antennas immersed in a cylindrical discharge plasma at two positions along an axial background magnetic field. The whistler wave frequency was swept from somewhat below and up to the electron cyclotron frequency ω(ce). As the frequency was swept, the wave was resonantly absorbed by the part of the electron phase space density which was Doppler shifted into resonance according to the relation ω - k([parallel])v([parallel]) = ω(ce). The measured absorption is directly related to the reduced parallel electron distribution function integrated along the wave trajectory. The background theory and initial results from this diagnostic are presented here. Though this diagnostic is best suited to detect tail populations of the parallel electron distribution function, these first results show that this diagnostic is also rather successful in measuring the bulk plasma density and temperature both during the plasma discharge and into the afterglow.
Whistler Waves Driven by Anisotropic Strahl Velocity Distributions: Cluster Observations
Vinas, A.F.; Gurgiolo, C.; Nieves-Chinchilla, T.; Gary, S. P.; Goldstein, M. L.
2010-01-01
Observed properties of the strahl using high resolution 3D electron velocity distribution data obtained from the Cluster/PEACE experiment are used to investigate its linear stability. An automated method to isolate the strahl is used to allow its moments to be computed independent of the solar wind core+halo. Results show that the strahl can have a high temperature anisotropy (T(perpindicular)/T(parallell) approximately > 2). This anisotropy is shown to be an important free energy source for the excitation of high frequency whistler waves. The analysis suggests that the resultant whistler waves are strong enough to regulate the electron velocity distributions in the solar wind through pitch-angle scattering
Mithaiwala, Manish; Crabtree, Chris; Ganguli, Gurudas
2012-01-01
It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore in the high-beta solar wind plasma whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave turbulence creates a plateau by quasilinear diffusion in the solar wind electron distribution at small velocities. It is found that for whistler energy density of only ~10^-3 that of the kinetic Alfven waves, the quasilinear diffusion rate due to whistlers is comparable to KAW. Thus very small amplitude whistler turbulence can have a significant consequence on the evolution of the solar wind electron distribution function.
Electron Scattering by High-Frequency Whistler Waves at Earth's Bow Shock
Oka, M.; Wilson, L. B., III; Phan, T. D.; Hull, A. J.; Amano, T.; Hoshino, M.; Argall, M. R.; Le Contel, O.; Agapitov, O.; Gersham, D. J.;
2017-01-01
Electrons are accelerated to non-thermal energies at shocks in space and astrophysical environments. While different mechanisms of electron acceleration have been proposed, it remains unclear how non-thermal electrons are produced out of the thermal plasma pool. Here, we report in situ evidence of pitch-angle scattering of non-thermal electrons by whistler waves at Earths bow shock. On 2015 November 4, the Magnetospheric Multiscale (MMS) mission crossed the bow shock with an Alfvn Mach number is approximately 11 and a shock angle of approximately 84deg. In the ramp and overshoot regions, MMS revealed bursty enhancements of non-thermal (0.52 keV) electron flux, correlated with high-frequency (0.2 - 0.4 Omega(sub ce), where Omega(sub ce) is the cyclotron frequency) parallel-propagating whistler waves. The electron velocity distribution (measured at 30 ms cadence) showed an enhanced gradient of phase-space density at and around the region where the electron velocity component parallel to the magnetic field matched the resonant energy inferred from the wave frequency range. The flux of 0.5 keV electrons (measured at 1ms cadence) showed fluctuations with the same frequency. These features indicate that non-thermal electrons were pitch-angle scattered by cyclotron resonance with the high-frequency whistler waves. However, the precise role of the pitch-angle scattering by the higher-frequency whistler waves and possible nonlinear effects in the electron acceleration process remains unclear.
Thermal effects on parallel resonance energy of whistler mode wave
Indian Academy of Sciences (India)
Devendraa Siingh; Shubha Singh; R P Singh
2006-02-01
In this short communication, we have evaluated the effect of thermal velocity of the plasma particles on the energy of resonantly interacting energetic electrons with the propagating whistler mode waves as a function of wave frequency and -value for the normal and disturbed magnetospheric conditions. During the disturbed conditions when the magnetosphere is depleted in electron density, the resonance energy of the electron enhances by an order of magnitude at higher latitudes, whereas the effect is small at low latitudes. An attempt is made to explain the enhanced wave activity observed during magnetic storm periods.
Whistler wave bursts upstream of the Uranian bow shock
Smith, Charles W.; Goldstein, Melvyn L.; Wong, Hung K.
1989-01-01
Observations of magnetic field wave bursts upstream of the Uranian bow shock are reported which were recorded prior to the inbound shock crossing. Three wave types are identified. One exhibits a broad spectral enhancement from a few millihertz to about 50 mHz and is seen from 17 to 10 hr prior to the inbound shock crossing. It is argued that these waves are whistler waves that have propagated upstream from the shock. A second wave type has a spacecraft frame frequency between 20 and 40 mHz, is seen only within or immediately upstream of the shock pedestal, is right-hand polarized in the spacecraft frame, and has a typical burst duration of 90 s. The third wave type has a spacecraft frame frequency of about 0.15 Hz, is seen exclusively within the shock pedestal, is left-hand polarized in the spacecraft frame, and has a burst duration lasting up to 4 min. It is argued that the low-frequency bursts are whistler waves with phase speed comparable to, but in excess of, the solar wind speed.
Generation mechanism of whistler waves produced by electron beam injection in space
Pritchett, P. L.; Karimabadi, H.; Omidi, N.
1989-01-01
Electromagnetic particle simulations are used to determine the generation mechanism of the whistler waves observed in connection with the artificial injection of electron beams in the ionosphere. The production of the waves is shown to be closely connected with the beam-plasma interaction, which leads to the formation of a current structure which acts like an antenna and emits the whistler waves in a coherent manner. This process, in contrast to a mechanism involving amplification of radiation by a whistler mode plasma instability within the beam, allows the whistlers to be generated even though the beam width is less than one wavelength.
New aspects of whistler waves driven by an electron beam studied by a 3-D electromagnetic code
Nishikawa, Ken-Ichi; Buneman, Oscar; Neubert, Torsten
1994-01-01
We have restudied electron beam driven whistler waves with a 3-D electromagnetic particle code. The simulation results show electromagnetic whistler wave emissions and electrostatic beam modes like those observed in the Spacelab 2 electron beam experiment. It has been suggested in the past that the spatial bunching of beam electrons associated with the beam mode may directly generate whistler waves. However, the simulation results indicate several inconsistencies with this picture: (1) whistler waves continue to be generated even after the beam mode space charge modulation looses its coherence, (2) the parallel (to the background magnetic field) wavelength of the whistler wave is longer than that of the beam instability, and (3) the parallel phase velocity of the whistler wave is smaller than that of the beam mode. The complex structure of the whistler waves in the vicinity of the beam suggest that the transverse motion (gyration) of the beam and background electrons is also involved in the generation of whistler waves.
New aspects of whistler waves driven by an electron beam studied by a 3-D electromagnetic code
Nishikawa, Ken-Ichi; Buneman, Oscar; Neubert, Torsten
1994-01-01
We have restudied electron beam driven whistler waves with a 3-D electromagnetic particle code. The simulation results show electromagnetic whistler wave emissions and electrostatic beam modes like those observed in the Spacelab 2 electron beam experiment. It has been suggested in the past that the spatial bunching of beam electrons associated with the beam mode may directly generate whistler waves. However, the simulation results indicate several inconsistencies with this picture: (1) whistler waves continue to be generated even after the beam mode space charge modulation looses its coherence, (2) the parallel (to the background magnetic field) wavelength of the whistler wave is longer than that of the beam instability, and (3) the parallel phase velocity of the whistler wave is smaller than that of the beam mode. The complex structure of the whistler waves in the vicinity of the beam suggest that the transverse motion (gyration) of the beam and background electrons is also involved in the generation of whistler waves.
Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere
Hsieh, Yi-Kai; Omura, Yoshiharu
2017-01-01
We perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave-particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =- 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (˜70°) and high energies (˜2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.
Whistler waves associated with the Uranian bow shock - Outbound observations
Smith, Charles W.; Wong, Hung K.; Goldstein, Melvyn L.
1991-01-01
High-resolution magnetic field measurements from the first outbound crossing of the Uranian bowshock by the Voyager 2 spacecraft between January 27 and 30, 1986, are examined. Evidence is found of enhanced whistler wave activity in the vicinity of three shock crossings but little or no evidence of such activity elsewhere. Two wave events display two separate and simultaneous wave enhancements each. From an investigation of these events using high-resolution field data, it is concluded that they are analogous to those whistler waves upstream of the earth's bow shock that are driven by beams of electrons. An instability analysis is presented to show that a single electron beam with reasonable parameters can penetrate both of the upstream and downstream of a shock crossing. This event displays only one relatively broad spectral enhancement in the same frequency regime and is left-hand polarized in the spacecraft frame. It is argued that this event is the result of a gyrating proton distribution associated with the oblique shock.
Whistler wave interaction with magnetic islands and electron scale structure formation
Pathak, Neha
2016-07-01
The present work aims to investigate the role of whistler waves in facilitating reconnection and to explore relationship between magnetic reconnection and turbulence. The key role of the whistler waves in the formation of coherent structures during their propagation in the pre-existing fully developed chain of magnetic islands has been investigated. For this scenario, the dynamical equation of whistler wave has been derived in the presence of magnetic islands and has been solved semi-analytically as well as numerically. Due to pre-existing magnetic islands, background field gets perturbed and localization of the whistler waves and formation of current sheets of electron scale takes place, contributing to the generation of magnetic turbulence. In this way whistler wave propagating through fully developed magnetic islands may provide a physical mechanism underlying the formation of electron scale current sheet.
Generation and detection of whistler wave induced space plasma turbulence at Gakona, Alaska
Rooker, L. A.; Lee, M. C.; Pradipta, R.; Watkins, B. J.
2013-07-01
We report on high-frequency wave injection experiments using the beat wave technique to study the generation of very-low-frequency (VLF) whistler waves in the ionosphere above Gakona, Alaska. This work is aimed at investigating whistler wave interactions with ionospheric plasmas and radiation belts. The beat wave technique involves injecting two X-mode waves at a difference frequency in the VLF range using the High-frequency Active Auroral Research Program (HAARP) heating facility. A sequence of beat wave-generated whistler waves at 2, 6.5, 7.5, 8.5, 9.5, 11.5, 15.5, 22.5, 28.5 and 40.5 kHz were detected in our 2011 experiments. We present Modular Ultra-high-frequency Ionospheric Radar (MUIR) (446 MHz) measurements of ion lines as the primary diagnosis of ionospheric plasma effects caused by beat wave-generated whistler waves. A magnetometer and digisonde were used to monitor the background ionospheric plasma conditions throughout the experiments. Our theoretical and data analyses show that VLF whistler waves can effectively interact with ionospheric plasmas via two different four-wave interaction processes leading to energization of electrons and ions. These preliminary results support our Arecibo experiments to study NAU-launched 40.75 kHz whistler wave interactions with space plasmas.
Wilson, Lynn B., III
2010-01-01
We present a statistical study of the characteristics of electron distributions associated with large amplitude whistler waves inside the terrestrial magnetosphere using waveform capture data as an addition of the study by Kellogg et al., [2010b]. We identified three types of electron distributions observed simultaneously with the whistler waves including beam-like, beam/flattop, and anisotropic distributions. The whistlers exhibited different characteristics dependent upon the observed electron distributions. The majority of the waveforms observed in our study have f/fce or = 8 nT pk-pk) whistler wave measured in the radiation belts. The majority of the largest amplitude whistlers occur during magnetically active periods (AE > 200 nT).
Cattell, Cynthia; Breneman, A.; Goetz, K.; Kellogg, P.; Kersten, K.; Wygant, J.; Wilson, L. B., III; Looper, Mark D.; Blake, J. Bernard; Roth, I.
2012-01-01
One of the critical problems for understanding the dynamics of Earth's radiation belts is determining the physical processes that energize and scatter relativistic electrons. We review measurements from the Wind/Waves and STEREO S/Waves waveform capture instruments of large amplitude whistler-mode waves. These observations have provided strong evidence that large amplitude (100s mV/m) whistler-mode waves are common during magnetically active periods. The large amplitude whistlers have characteristics that are different from typical chorus. They are usually nondispersive and obliquely propagating, with a large longitudinal electric field and significant parallel electric field. We will also review comparisons of STEREO and Wind wave observations with SAMPEX observations of electron microbursts. Simulations show that the waves can result in energization by many MeV and/or scattering by large angles during a single wave packet encounter due to coherent, nonlinear processes including trapping. The experimental observations combined with simulations suggest that quasilinear theoretical models of electron energization and scattering via small-amplitude waves, with timescales of hours to days, may be inadequate for understanding radiation belt dynamics.
Whistler mode waves and the electron heat flux in the solar wind: cluster observations
Energy Technology Data Exchange (ETDEWEB)
Lacombe, C.; Alexandrova, O.; Cornilleau-Wehrlin, N.; Mangeney, A.; De Conchy, Y.; Maksimovic, M. [LESIA, Observatoire de Paris, PSL Research University, CNRS, UPMC Université Paris 06, Université Paris-Diderot, 5 Place Jules Janssen, F-92190 Meudon (France); Matteini, L. [Imperial College, London SW7 2AZ (United Kingdom); Santolík, O. [Institute of Atmospheric Physics ASCR, 141 31 Prague (Czech Republic)
2014-11-20
The nature of the magnetic field fluctuations in the solar wind between the ion and electron scales is still under debate. Using the Cluster/STAFF instrument, we make a survey of the power spectral density and of the polarization of these fluctuations at frequencies f in [1, 400] Hz, during five years (2001-2005), when Cluster was in the free solar wind. In ∼10% of the selected data, we observe narrowband, right-handed, circularly polarized fluctuations, with wave vectors quasi-parallel to the mean magnetic field, superimposed on the spectrum of the permanent background turbulence. We interpret these coherent fluctuations as whistler mode waves. The lifetime of these waves varies between a few seconds and several hours. Here, we present, for the first time, an analysis of long-lived whistler waves, i.e., lasting more than five minutes. We find several necessary (but not sufficient) conditions for the observation of whistler waves, mainly a low level of background turbulence, a slow wind, a relatively large electron heat flux, and a low electron collision frequency. When the electron parallel beta factor β {sub e∥} is larger than 3, the whistler waves are seen along the heat flux threshold of the whistler heat flux instability. The presence of such whistler waves confirms that the whistler heat flux instability contributes to the regulation of the solar wind heat flux, at least for β {sub e∥} ≥ 3, in slow wind at 1 AU.
Propagation and dispersion of whistler waves generated by fast reconnection onset
Singh, Nagendra
2013-02-01
The role of whistler mode during the onset of magnetic reconnection (MR) has been widely suggested, but the manifestations of its highly dispersive and anisotropic propagation properties in reconnection events remain largely unclear. Comparing results from a recently developed theoretical model for reconnection in terms of whistler's dispersive behavior with those reported from laboratory experiments on fast spontaneous magnetic reconnection, we demonstrate that the onset of fast reconnection in electron current layers (ECLs) emits whistler wave packets. The time scale of the explosively fast reconnection events are inversely related to the whistler mode frequencies at the lower end of the whistler frequency band. The wave packets in this frequency band have a characteristic angular dispersion, which marks the initial opening of the reconnection exhaust angle. The multidimensional propagation of the whistler for the reconnection with a strong guide magnetic field is investigated, showing that the measured propagation velocities of the reconnection electric field along the guide field in the Versatile Toroidal Facility at MIT quantitatively compare with the group velocities of the whistler wave packets. The whistler mode dispersive properties measured in laboratory experiments without a guide magnetic field in the magnetic reconnection experiments at Princeton also compare well with the theoretically predicted dispersion of the wave packets depending on the ECL width. Fast normalized reconnection rates extending to ˜0.35 at the MR onset in thin ECLs imply whistler wave propagation away from the onset location. We also present evidences for the whistler wave packets being emitted from reconnection diffusion region as seen in simulations and satellite observations.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina; Tsiklauri, David
2014-05-01
]. In this study [5], for the first time, the backwards propagating wave component evident in the perpendicular components of the electromagnetic field in such a system is presented. Features of the wave component propagating backwards from the front of the non-gyrotropic, relativistic, beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile are studied by using the Particle-In-Cell code EPOCH. Magnetic field in the 1.5-dimensional system is varied in order to prove that the backwards propagating wave is harmonic of the electron cyclotron frequency. The analysis has lead to the identification of the backwards travelling waves as whistlers. Moreover, the whistlers are shown to be generated by the normal and anomalous Doppler resonance. Large fraction of the energy of the perpendicular electromagnetic field components is found to be carried away by the whistler waves. [1] D. Tsiklauri, Phys. Plasmas 18, 052903 (2011). [2] D. Tsiklauri, H. Schmitz, Geophys. Res. Abs. 15, EGU2013-5403 (2013). [3] H. Schmitz, D. Tsiklauri, Phys. Plasmas 20, 062903 (2013). [4] R. Pechhacker, D. Tsiklauri, Phys. Plasmas 19, 112903 (2012). [5] M. Skender, D. Tsiklauri, submitted to Phys. Plasmas (2013): http://astro.qmul.ac.uk/ tsiklauri/
Nonlinear penetration of whistler pulses into collisional plasmas via conductivity modifications
Urrutia, J. M.; Stenzel, R. L.
1991-01-01
A strong electromagnetic impulse (about 0.2 microsec) with central frequency in the whistler-wave regime is applied to a large laboratory plasma dominated by Coulomb collisions. Local electron heating at the antenna and transport along B0 create a channel of high conductivity along which the whistler pulse penetrates with little damping. Because of its rapid temporal evolution, this new form of modulational instability does not involve ducting by density gradients which require ion time scales to develop.
Diffusion of radiation belt protons by whistler waves
Energy Technology Data Exchange (ETDEWEB)
Villalon, E.; Burke, W.J.
1994-11-01
Whistler waves propagating near the quasi-electrostatic limit can interact with energetic protons (appr. 80 - 500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate obliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker-Planck equation is integrated along the flux tube considering the contributions of multiple-resonance crossings. The quasi-linear diffusion coefficients in energy, cross energy/pitch angle, and pitch angle are obtalned for second order resonant interactions. They are shown to be proportional to the electric fields amplitudes. Numerical calculations for the second order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments.
Diffusion of radiation belt protons by whistler waves
Villalon, Elena; Burke, William J.
1994-11-01
Whistler waves propagating near the quasi-electrostatic limit can interact with energetic protons (approximately 80 - 500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate obliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker-Planck equation is intergrated along the flux tube considering the contributions of multiple-resonance crossings. The quasi-linear diffusion coefficients in energy, cross energy/ pitch angle, and pitch angle are obtained for second-order resonant interactions. They are sown to be proportional to the electric fields amplitudes. Numerical calculations for the second-order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/ pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments.
Diffusion of radiation belt protons by whistler waves
Energy Technology Data Exchange (ETDEWEB)
Villalon, E. [Northeastern Univ., Boston, MA (United States); Burke, W.J. [Hanscom Air Force Base, MA (United States)
1994-11-01
Whistler waves propagating near the quasi-electrostatic limit can interact with energetic protons ({approximately}80-500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate oliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker-Planck equation is integrated along the flux tube considering the contributions of multiple-resonance crossings. The quasi-linear diffusion coefficients in energy, cross energy/pitch angle, and pitch angle are obtained for second-order resonant interactions. They are shown to be proportional to the electric fields amplitudes. Numerical calculations for the second-order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments. 24 refs., 12 figs.
Saito, Shinji; Miyoshi, Yoshizumi; Seki, Kanako
2016-07-01
Wave-particle interactions with whistler chorus waves are believed to provide a primary acceleration for electrons in the outer radiation belt. Previous models for flux enhancement of the radiation belt have assumed the stochastic process as a diffusion manner of successive random-phase interactions, but physical mechanisms for the acceleration are not fully incorporated in these models because of the lack of a nonlinear scattering process. Here we report rapid increase in relativistic electron flux by using an innovative computer simulation model that incorporates not only diffusive process but also nonlinear scattering processes. The simulations show that three types of scattering simultaneously occur, which are diffusive, phase trapping, and phase bunching. It is found that the phase trapping is the most efficient mechanism to produce the MeV electrons rapidly in the scattering processes. The electrons are accelerated from 400 keV to over 1 MeV in time scale less than 60 s. On the other hand, as the phase trapping is suppressed by the breaking of relative phase angle between waves and gyrating electrons during the interaction, the increase of electron flux at MeV energy is clearly reduced. Our simulations conclude that the phase-trapping process causes a significant effect for the increase in relativistic electron flux and suggest that a quasi-linear diffusion model is not always valid to fully describe the relativistic electron acceleration.
Energy Technology Data Exchange (ETDEWEB)
Winske, D., E-mail: winske@lanl.gov; Daughton, W. [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2015-02-15
We present results of three-dimensional electromagnetic particle-in-cell simulations of the lower hybrid ion ring instability, similar to our earlier results [D. Winske and W. Daughton, Phys. Plasma 19, 072109 (2012)], but at higher electron beta (β{sub e} = ratio of electron thermal pressure to magnetic pressure = 0.06, rather than at 0.006) with T{sub i} = T{sub e}. At higher electron beta, the level of lower hybrid waves at saturation normalized to the ion thermal energy (β{sub i} = 0.06 also) is only slightly smaller, but the corresponding magnetic fluctuations are about an order of magnitude larger, consistent with linear theory. After saturation, the waves evolve into whistler waves, through a number of possible mechanisms, with an average growth rate considerably smaller than the linear growth rate of the lower hybrid waves, to a peak fluctuation level that is about 20% above the lower hybrid wave saturation level. The ratio of the peak magnetic fluctuations associated with the whistler waves relative to those of the saturated lower hybrid waves, the ratio of the nonlinear growth rate of whistlers relative to the linear growth rate of lower hybrid waves, the amount of energy extracted from the ring, and the amount of heating of the background ions and electrons are comparable to those in the lower electron beta 3D simulation. This suggests that even at higher electron beta, the linear and nonlinear physics of the lower hybrid ion ring instability is dominated by electrostatic, wave-particle rather than wave-wave interactions.
Winske, D.; Daughton, W.
2015-02-01
We present results of three-dimensional electromagnetic particle-in-cell simulations of the lower hybrid ion ring instability, similar to our earlier results [D. Winske and W. Daughton, Phys. Plasma 19, 072109 (2012)], but at higher electron beta (βe = ratio of electron thermal pressure to magnetic pressure = 0.06, rather than at 0.006) with Ti = Te. At higher electron beta, the level of lower hybrid waves at saturation normalized to the ion thermal energy (βi = 0.06 also) is only slightly smaller, but the corresponding magnetic fluctuations are about an order of magnitude larger, consistent with linear theory. After saturation, the waves evolve into whistler waves, through a number of possible mechanisms, with an average growth rate considerably smaller than the linear growth rate of the lower hybrid waves, to a peak fluctuation level that is about 20% above the lower hybrid wave saturation level. The ratio of the peak magnetic fluctuations associated with the whistler waves relative to those of the saturated lower hybrid waves, the ratio of the nonlinear growth rate of whistlers relative to the linear growth rate of lower hybrid waves, the amount of energy extracted from the ring, and the amount of heating of the background ions and electrons are comparable to those in the lower electron beta 3D simulation. This suggests that even at higher electron beta, the linear and nonlinear physics of the lower hybrid ion ring instability is dominated by electrostatic, wave-particle rather than wave-wave interactions.
Artemyev, Anton; Agapitov, Oleksiy; Mourenas, Didier; Krasnoselskikh, Vladimir; Shastun, Vitalii; Mozer, Forrest
2016-04-01
In this paper we review recent spacecraft observations of oblique whistler-mode waves in the Earth's inner magnetosphere as well as the various consequences of the presence of such waves for electron scattering and acceleration. In particular, we survey the statistics of occurrences and intensity of oblique chorus waves in the region of the outer radiation belt, comprised between the plasmapause and geostationary orbit, and discuss how their actual distribution may be explained by a combination of linear and non-linear generation, propagation, and damping processes. We further examine how such oblique wave populations can be included into both quasi-linear diffusion models and fully nonlinear models of wave-particle interaction. On this basis, we demonstrate that varying amounts of oblique waves can significantly change the rates of particle scattering, acceleration, and precipitation into the atmosphere during quiet times as well as in the course of a storm. Finally, we discuss possible generation mechanisms for such oblique waves in the radiation belts. We demonstrate that oblique whistler-mode chorus waves can be considered as an important ingredient of the radiation belt system and can play a key role in many aspects of wave-particle resonant interactions.
Whistler wave-induced ionospheric plasma turbulence: Source mechanisms and remote sensing
Pradipta, R.; Rooker, L. A.; Whitehurst, L. N.; Lee, M. C.; Ross, L. M.; Sulzer, M. P.; Gonzalez, S.; Tepley, C.; Aponte, N.; See, B. Z.; Hu, K. P.
2013-10-01
We report a series of experiments conducted at Arecibo Observatory in the past, aimed at the investigation of 40.75 kHz whistler wave interactions with ionospheric plasmas and the inner radiation belts at L=1.35. The whistler waves are launched from a Naval transmitter (code-named NAU) operating in Aguadilla, Puerto Rico at the frequency and power of 40.75 kHz and 100 kW, respectively. Arecibo radar, CADI, and optical instruments were used to monitor the background ionospheric conditions and detect the induced ionospheric plasma effects. Four-wave interaction processes produced by whistler waves in the ionosphere can excite lower hybrid waves, which can accelerate ionospheric electrons. Furthermore, whistler waves propagating into the magnetosphere can trigger precipitation of energetic electrons from the radiation belts. Radar and optical measurements can distinguish wave-wave and wave-particle interaction processes occurring at different altitudes. Electron acceleration by different mechanisms can be verified from the radar measurements of plasma lines. To facilitate the coupling of NAU-launched 40.75 kHz whistler waves into the ionosphere, we can rely on naturally occurring spread F irregularities to serve as ionospheric ducts. We can also use HF wave-created ducts/artificial waveguides, as demonstrated in our earlier Arecibo experiments and recent Gakona experiments at HAARP. The newly constructed Arecibo HF heater will be employed in our future experiments, which can extend the study of whistler wave interactions with the ionosphere and the magnetosphere/radiation belts as well as the whistler wave conjugate propagation between Arecibo and Puerto Madryn, Argentina.
Large Amplitude Whistlers in the Magnetosphere Observed with Wind-Waves
Kellogg, P. J.; Cattell, C. A.; Goetz, K.; Monson, S. J.; Wilson, L. B., III
2011-01-01
We describe the results of a statistical survey of Wind-Waves data motivated by the recent STEREO/Waves discovery of large-amplitude whistlers in the inner magnetosphere. Although Wind was primarily intended to monitor the solar wind, the spacecraft spent 47 h inside 5 R(sub E) and 431 h inside 10 R(sub E) during the 8 years (1994-2002) that it orbited the Earth. Five episodes were found when whistlers had amplitudes comparable to those of Cattell et al. (2008), i.e., electric fields of 100 m V/m or greater. The whistlers usually occurred near the plasmapause. The observations are generally consistent with the whistlers observed by STEREO. In contrast with STEREO, Wind-Waves had a search coil, so magnetic measurements are available, enabling determination of the wave vector without a model. Eleven whistler events with useable magnetic measurements were found. The wave vectors of these are distributed around the magnetic field direction with angles from 4 to 48deg. Approximations to observed electron distribution functions show a Kennel-Petschek instability which, however, does not seem to produce the observed whistlers. One Wind episode was sampled at 120,000 samples/s, and these events showed a signature that is interpreted as trapping of electrons in the electrostatic potential of an oblique whistler. Similar waveforms are found in the STEREO data. In addition to the whistler waves, large amplitude, short duration solitary waves (up to 100 mV/m), presumed to be electron holes, occur in these passes, primarily on plasma sheet field lines mapping to the auroral zone.
On the role of ion-scale whistler waves in space and astrophysical plasma turbulence
Comişel, Horia; Nariyuki, Yasuhiro; Narita, Yasuhito; Motschmann, Uwe
2016-11-01
Competition of linear mode waves is studied numerically to understand the energy cascade mechanism in plasma turbulence on ion-kinetic scales. Hybrid plasma simulations are performed in a text">3-D simulation box by pumping large-scale Alfvén waves on the fluid scale. The result is compared with that from our earlier text">2-D simulations. We find that the whistler mode is persistently present both in the text">2-D and text">3-D simulations irrespective of the initial setup, e.g., the amplitude of the initial pumping waves, while all the other modes are excited and damped such that the energy is efficiently transported to thermal energy over non-whistler mode. The simulation results suggest that the whistler mode could transfer the fluctuation energy smoothly from the fluid scale down to the electron-kinetic scale, and justifies the notion of whistler turbulence.
Energetic Electron Pitch Angle Diffusion due to Whistler Wave during Terrestrial Storms
Institute of Scientific and Technical Information of China (English)
XIAO Fu-Liang; HE Hui-Yong
2006-01-01
A concise and elegant expression of cyclotron harmonic resonant quasi-pure pitch-angle diffusion is constructed for the parallel whistler mode waves, and the quasi-linear diffusion coefficient is prescribed in terms of the whistler mode wave spectral intensity. Numerical computations are performed for the specific case of energetic electrons interacting with a band of frequency of whistler mode turbulence at L ≈ 3. It is found that the quasi-pure pitch-angle diffusion driven by the whistler mode scatters energetic electrons from the larger pitch-angles into the loss cone, and causes pitch-angle distribution to evolve from the pancake-shaped before the terrestrial storms to the flat-top during the main phase. This probably accounts for the quasi-isotropic pitch-angle distribution observed by the combined release and radiation effects satellite spacecraft at L ≈ 3.
Energy Technology Data Exchange (ETDEWEB)
Es’kin, V. A.; Zaboronkova, T. M.; Kudrin, A. V., E-mail: kud@rf.unn.ru; Ostafiychuk, O. M. [Lobachevskii State University of Nizhni Novgorod (Russian Federation)
2015-03-15
Guidance of azimuthally symmetric waves by cylindrical density ducts in magnetoplasma in the nonresonant region of the whistler frequency range is investigated. It is demonstrated that eigenmodes existing at the studied frequencies in ducts with enhanced plasma density allow simplified description that makes analysis of the features of their guided propagation much easier. The results of calculation of the dispersion characteristics and field structure of the whistler modes supported by such ducts are presented.
2009-03-30
These observations will be compared with raytracing models. These analyses will determine the controlling factors of the coupling between the...ionosphere and magnetosphere, and the propagation characteristics of whistler waves in space, verify the raytracing models, and provide guidance for... raytracing model improvements when necessary. Correctly modeling whistler wave propagation in the magnetosphere as functions of plasma conditions and wave
Generation of whistler-wave heated discharges with planar resonant RF networks.
Guittienne, Ph; Howling, A A; Hollenstein, Ch
2013-09-20
Magnetized plasma discharges generated by a planar resonant rf network are investigated. A regime transition is observed above a magnetic field threshold, associated with rf waves propagating in the plasma and which present the characteristics of whistler waves. These wave heated regimes can be considered as analogous to conventional helicon discharges, but in planar geometry.
Van Compernolle, B; Bortnik, J; Pribyl, P; Gekelman, W; Nakamoto, M; Tao, X; Thorne, R M
2014-04-11
Resonant interactions between energetic electrons and whistler mode waves are an essential ingredient in the space environment, and in particular in controlling the dynamic variability of Earth's natural radiation belts, which is a topic of extreme interest at the moment. Although the theory describing resonant wave-particle interaction has been present for several decades, it has not been hitherto tested in a controlled laboratory setting. In the present Letter we report on the first laboratory experiment to directly detect resonant pitch angle scattering of energetic (∼keV) electrons due to whistler mode waves. We show that the whistler mode wave deflects energetic electrons at precisely the predicted resonant energy, and that varying both the maximum beam energy, and the wave frequency, alters the energetic electron beam very close to the resonant energy.
Directory of Open Access Journals (Sweden)
G. Stenberg
2007-11-01
Full Text Available We use whistler waves observed close to the magnetopause as an instrument to investigate the internal structure of the magnetopause-magnetosheath boundary layer. We find that this region is characterized by tube-like structures with dimensions less than or comparable with an ion inertial length in the direction perpendicular to the ambient magnetic field. The tubes are revealed as they constitute regions where whistler waves are generated and propagate. We believe that the region containing tube-like structures extend several Earth radii along the magnetopause in the boundary layer. Within the presumed wave generating regions we find current structures moving at the whistler wave group velocity in the same direction as the waves.
Experimental determination of whistler wave dispersion relation in the solar wind
Stansby, D; Chen, C H K; Matteini, L
2016-01-01
The origins and properties of large amplitude whistler wave packets in the solar wind are still unclear. In this Letter we utilise single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wave packets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarised, travel anti-sunward and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.
Semiannual Status Report. [excitation of electromagnetic waves in the whistler frequency range
1994-01-01
During the last six months, we have continued our study of the excitation of electromagnetic waves in the whistler frequency range and the role that these waves will play in the acceleration of electrons and ions in the auroral region. A paper entitled 'Electron Beam Excitation of Upstream Waves in the Whistler Mode Frequency Range' was listed in the Journal of Geophysical Research. In this paper, we have shown that an anisotropic electron beam (or gyrating electron beam) is capable of generating both left-hand and right-hand polarized electromagnetic waves in the whistler frequency range. Since right-hand polarized electromagnetic waves can interact with background electrons and left-hand polarized waves can interact with background ions through cyclotron resonance, it is possible that these beam generated left-hand and right-hand polarized electromagnetic waves can accelerate either ions or electrons (or both), depending on the physical parameters under consideration. We are currently carrying out a comprehensive study of the electromagnetic whistler and lower hybrid like waves observed in the auroral zone using both wave and particle data. Our first task is to identify these wave modes and compare it with particle observations. Using both the DE-1 particle and wave measurements, we can positively identify those electromagnetics lower hybrid like waves as fast magnetosonic waves and the upper cutoff of these waves is the local lower hybrid frequency. From the upper cutoff of the frequency spectrum, one can infer the particle density and the result is in very good agreement with the particle data. Since these electromagnetic lower hybrid like waves can have frequencies extended down to the local ion cyclotron frequency, it practically confirms that they are not whistler waves.
Semiannual Status Report. [excitation of electromagnetic waves in the whistler frequency range
1994-01-01
During the last six months, we have continued our study of the excitation of electromagnetic waves in the whistler frequency range and the role that these waves will play in the acceleration of electrons and ions in the auroral region. A paper entitled 'Electron Beam Excitation of Upstream Waves in the Whistler Mode Frequency Range' was listed in the Journal of Geophysical Research. In this paper, we have shown that an anisotropic electron beam (or gyrating electron beam) is capable of generating both left-hand and right-hand polarized electromagnetic waves in the whistler frequency range. Since right-hand polarized electromagnetic waves can interact with background electrons and left-hand polarized waves can interact with background ions through cyclotron resonance, it is possible that these beam generated left-hand and right-hand polarized electromagnetic waves can accelerate either ions or electrons (or both), depending on the physical parameters under consideration. We are currently carrying out a comprehensive study of the electromagnetic whistler and lower hybrid like waves observed in the auroral zone using both wave and particle data. Our first task is to identify these wave modes and compare it with particle observations. Using both the DE-1 particle and wave measurements, we can positively identify those electromagnetics lower hybrid like waves as fast magnetosonic waves and the upper cutoff of these waves is the local lower hybrid frequency. From the upper cutoff of the frequency spectrum, one can infer the particle density and the result is in very good agreement with the particle data. Since these electromagnetic lower hybrid like waves can have frequencies extended down to the local ion cyclotron frequency, it practically confirms that they are not whistler waves.
Whistler mode waves driven by anisotropic electrons in the Martian magnetosphere
Harada, Y.; Andersson, L.; Fowler, C. M.; Mitchell, D. L.; Halekas, J. S.; Mazelle, C. X.; Espley, J. R.; DiBraccio, G. A.; McFadden, J. P.; Brain, D. A.; Xu, S.; Ruhunusiri, S.; Larson, D. E.; Lillis, R. J.; Hara, T.; Livi, R.; Jakosky, B. M.
2016-12-01
We present MAVEN observations of narrowband electromagnetic waves at frequencies between the local electron cyclotron and lower hybrid frequencies in the Martian magnetosphere. Although Phobos-2 first measured bursts of electric field waves below the electron cyclotron frequency, the lack of magnetic field wave data hindered definitive identification of the wave mode and generation mechanisms. We analyze electric and magnetic field wave spectra obtained by MAVEN and demonstrate that the observed narrowband waves have properties consistent with whistler mode. We utilize electron measurements to compute linear growth rates of whistler mode and show that cyclotron resonance with anisotropic electrons on open and closed field lines can produce the observed narrowband features. Additionally, a statistical survey reveals that the narrowband wave events and anisotropic electrons have similar spatial distributions, providing further support for this scenario. Interestingly, some of the observed waves display complex frequency-time structures that resemble whistler-mode chorus waves in the terrestrial inner magnetosphere, including discrete elements of rising tones and two bands above and below half the electron cyclotron frequency. Whistler mode waves driven by anisotropic electrons, previously observed in intrinsic magnetospheres and at unmagnetized airless bodies, are now confirmed by MAVEN at Mars.
Second-Order Resonant Interaction of Ring Current Protons with Whistler-Mode Waves
Institute of Scientific and Technical Information of China (English)
XIAO Fu-Liang; CHEN Liang-Xu; HE Hui-Yong; ZHOU Qing-Hua
2008-01-01
We present a study on the second-order resonant interaction between the ring current protons with Whistler-mode waves propagating near the quasi electrostatic limit following the previous second-order resonant theory.The diffusion coefficients are proportional to the electric field amplitude E,much greater than those for the regular first-order resonance.which are proportional to the electric field amplitudes square E2.Numerical calculations for the pitch angle scattering are performed for typical energies of protons Ek=50ke V and 100ke V at locations L=2 and L=3.5.The timescale for the loss process of protons by the Whistler waves is found to approach one hour,comparable to that by the EMIC waves,suggesting that Whistler waves may also contribute significantly to the ring current decay under appropriate conditions.
Modeling whistler wave generation regimes in magnetospheric cyclotron maser
Directory of Open Access Journals (Sweden)
D. L. Pasmanik
2004-11-01
quasi-periodic whistler wave emissions is verified.
Energy Technology Data Exchange (ETDEWEB)
Li, Jinxing, E-mail: lijx@pku.edu.cn [Institute of Space Physics and Applied Technology, Peking University, Beijing 100871 (China); Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095 (United States); Bortnik, Jacob; Thorne, Richard M. [Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095 (United States); Xie, Lun, E-mail: xielun@pku.edu.cn; Pu, Zuyin; Fu, Suiyan; Guo, Ruilong [Institute of Space Physics and Applied Technology, Peking University, Beijing 100871 (China); Chen, Lunjin [W. B. Hanson Center for Space Sciences, Department of Physics, University of Texas at Dallas, Richardson, Texas 75080 (United States); Ni, Binbin [Department of Space Physics, School of Electronic Information, Wuhan University, Wuhan, Hubei 430072 (China); Tao, Xin [Department of Geophysics and Planetary Sciences, University of Science and Technology of China, Hefei, Anhui 230026 (China); Yao, Zhonghua [Mullard Space Science Laboratory, University College London, Dorking (United Kingdom)
2015-05-15
Test particle simulation is a useful method for studying both linear and nonlinear wave-particle interactions in the magnetosphere. The gyro-averaged equations of particle motion for first-order and other cyclotron harmonic resonances with oblique whistler-mode waves were first derived by Bell [J. Geophys. Res. 89, 905 (1984)] and the most recent relativistic form was given by Ginet and Albert [Phys. Fluids B 3, 2994 (1991)], and Bortnik [Ph.D. thesis (Stanford University, 2004), p. 40]. However, recently we found there was a (−1){sup l−1} term difference between their formulas of perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force.
DE-1 and COSMOS 1809 observations of lower hybrid waves excited by VLF whistler mode waves
Bell, T. F; Inan, U. S.; Lauben, D.; Sonwalkar, V. S.; Helliwell, R. A.; Sobolev, Ya. P.; Chmyrev, V. M.; Gonzalez, S.
1994-01-01
Past work demostrates that strong lower hybrid (LH) waves can be excited by electromagnetic whistler mode waves throughout large regions of the topside ionosphere and magnetosphere. The effects of the excited LH waves upon the suprathermal ion population in the topside ionosphere and magnetosphere depend upon the distribution of LH wave amplitude with wavelength lambda. The present work reports plasma wave data from the DE-1 and COSMOS 1809 spacecraft which suggests that the excited LH wave spectrum has components for which lambda less than or equal to 3.5 m when excitation occurs at a frequency roughly equal to the local lower hybrid resonance frequency. This wavelength limit is a factor of approximately 3 below that reported in past work and suggests that the excited LH waves can interact with suprathermal H(+) ions with energy less than or equal to 6 eV. This finding supports recent work concerning the heating of suprathermal ions above thunderstorm cells.
Interaction of suprathermal solar wind electron fluxes with sheared whistler waves: fan instability
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C. Krafft
Full Text Available Several in situ measurements performed in the solar wind evidenced that solar type III radio bursts were some-times associated with locally excited Langmuir waves, high-energy electron fluxes and low-frequency electrostatic and electromagnetic waves; moreover, in some cases, the simultaneous identification of energetic electron fluxes, Langmuir and whistler waves was performed. This paper shows how whistlers can be excited in the disturbed solar wind through the so-called "fan instability" by interacting with energetic electrons at the anomalous Doppler resonance. This instability process, which is driven by the anisotropy in the energetic electron velocity distribution along the ambient magnetic field, does not require any positive slope in the suprathermal electron tail and thus can account for physical situations where plateaued reduced electron velocity distributions were observed in solar wind plasmas in association with Langmuir and whistler waves. Owing to linear calculations of growth rates, we show that for disturbed solar wind conditions (that is, when suprathermal particle fluxes propagate along the ambient magnetic field, the fan instability can excite VLF waves (whistlers and lower hybrid waves with characteristics close to those observed in space experiments.
Key words. Space plasma physics (waves and instabilities – Radio Science (waves in plasma – Solar physics, astrophysics and astronomy (radio emissions
Experimental Determination of Whistler Wave Dispersion Relation in the Solar Wind
Stansby, D.; Horbury, T. S.; Chen, C. H. K.; Matteini, L.
2016-09-01
The origins and properties of large-amplitude whistler wavepackets in the solar wind are still unclear. In this Letter, we utilize single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wavepackets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarized, travel anti-sunward, and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.
Whistler waves produced by a modulated electron beam: Electromagnetic fields in the linear approach
Energy Technology Data Exchange (ETDEWEB)
Volokitin, A. [Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Academy of Sciences, Troitsk, Moscow Region, 142092 (Russian Federation); Krafft, C.; Matthieussent, G. [Laboratoire de Physique des Gaz et des Plasmas, Universite Paris Sud, Centre National de la Recherche Scientifique, 91405 Orsay Cedex (France)
1995-11-01
The theory of whistler wave interaction with a modulated electron beam of finite radius and injected parallel to the magnetic field in an unbounded space plasma is considered. The study of the energy transfer between the thin beam and the whistler wave is done in the case of sheared whistlers, when the parallel wave number is very small compared to the perpendicular one. In this case, and in the linear regime, structures of potentials and electromagnetic fields inside and outside the beam are determined analytically. In the vicinity of the beam, simple expressions for field components are provided in the case of {hacek C}erenkov resonance near the double pole. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Emission of Whistler-mode waves and diffusion of electrons around interplanetary shocks
Pierre, F.; Solomon, J.; Cornilleau-Wehrlin, N.; Canu, P.; Scime, E. E.; Phillips, J. L.; Balogh, A.; Forsyth, R.
1995-01-01
Whistler-mode wave emissions are frequently observed at and downstream of interplanetary shocks. Using electron distribution functions measured onboard Ulysses in the energy range 1.6 to 862 eV, we calculate the temperature anisotropy and the wave growth rate of the electromagnetic electron cyclotron instability, Results of the calculations are compared to the whistler wave spectra observed simultaneously. For the studied events there is a good correlation between the wave growth rates and the wave spectra. Particularly, upstream of the shock front where no wave emissions are observed, the anisotropy lies below the wave instability threshold, i.e. the critical anisotropy Ac; on the contrary, downstream of the shock, the anisotropy exceeds Ac in some frequency range. Moreover. the tact that the anisotropy is close to Ac in a large frequency range gives prominence to the effect of velocity space diffusion of the electrons by the waves.
Quasi-parallel whistler mode waves observed by THEMIS during near-earth dipolarizations
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O. Le Contel
2009-06-01
Full Text Available We report on quasi-parallel whistler emissions detected by the near-earth satellites of the THEMIS mission before, during, and after local dipolarization. These emissions are associated with an electron temperature anisotropy α=T_{⊥e}/T_{||e}>1 consistent with the linear theory of whistler mode anisotropy instability. When the whistler mode emissions are observed the measured electron anisotropy varies inversely with β_{||e} (the ratio of the electron parallel pressure to the magnetic pressure as predicted by Gary and Wang (1996. Narrow band whistler emissions correspond to the small α existing before dipolarization whereas the broad band emissions correspond to large α observed during and after dipolarization. The energy in the whistler mode is leaving the current sheet and is propagating along the background magnetic field, towards the Earth. A simple time-independent description based on the Liouville's theorem indicates that the electron temperature anisotropy decreases with the distance along the magnetic field from the equator. Once this variation of α is taken into account, the linear theory predicts an equatorial origin for the whistler mode. The linear theory is also consistent with the observed bandwidth of wave emissions. Yet, the anisotropy required to be fully consistent with the observations is somewhat larger than the measured one. Although the discrepancy remains within the instrumental error bars, this could be due to time-dependent effects which have been neglected. The possible role of the whistler waves in the substorm process is discussed.
Kuo, S. P.
2008-10-01
An optimal approach reducing the population of MeV electrons in the magnetosphere is presented. Under a double resonance condition, whistler wave is simultaneously in cyclotron resonance with keV and MeV electrons. The injected whistler waves is first amplified by the background keV electrons via loss-cone negative mass instability to become effective in precipitating MeV electrons via cyclotron resonance elevated chaotic scattering. The numerical results show that a small amplitude whistler wave can be amplified by more than 25 dB. The amplification factor reduces only about 10 dB with a 30 dB increase of the initial wave intensity. Use of an amplified whistler wave to scatter 1.5 MeV electrons from an initial pitch angle of 86.5°to a pitch angle <50° is demonstrated. The ratio of the required wave magnetic field to the background magnetic field is calculated to be about 8×10-4.
The propagation and growth of whistler mode waves generated by electron beams in earth's bow shock
Tokar, R. L.; Gurnett, D. A.
1985-01-01
In this study, the propagation and growth of whistler mode waves generated by electron beams within earth's bow shock is investigated using a planar model for the bow shock and a model electron distribution function. Within the shock, the model electron distribution function possesses a field-aligned T greater than T beam that is directed toward the magnetosheath. Waves with frequencies between about 1 and 100 Hz with a wide range of wave normal angles are generated by the beam via Landau and anomalous cyclotron resonances. However, because the growth rate is small and because the wave packets traverse the shock quickly, these waves do not attain large amplitudes. Waves with frequencies between about 30 and 150 Hz with a wide range of wave normal angles are generated by the beam via the normal cyclotron resonance. The ray paths for most of these waves are directed toward the solar wind although some wave packets, due to plasma convection travel transverse to the shock normal. These wave packets grow to large amplitudes because they spend a long time in the growth region. The results suggest that whistler mode noise within the shock should increase in amplitude with increasing upstream theta sub Bn. The study provides an explanation for the origin of much of the whistler mode turbulence observed at the bow shock.
Tripathi, A. K.; Singhal, R. P.; Singh, K. P.; Singh, O. N.
2013-05-01
Bounce-averaged pitch angle diffusion coefficients of electrons due to resonant interaction with electrostatic electron cyclotron harmonic (ECH) and whistler mode waves have been calculated. Temporal growth rates obtained by solving the appropriate dispersion relation have been used to represent the distribution of wave energy with frequency. Calculations have been performed at two spatial locations L=4.6 and L=6.8. The results obtained suggest that ECH waves can put electrons on strong pitch angle diffusion at both spatial locations. However, at L=4.6, electrons with energy <100 eV and at L=6.8 electrons with energy up to ∼500 eV can be put on strong diffusion contributing to diffuse auroral precipitation. Whistler mode waves can put electrons of energy ≤5 keV on strong pitch angle diffusion at L=6.8 whereas at L=4.6 observed wave fields are insufficient to put electrons on strong diffusion. ECH waves contribute up to 17% of the total electron energy precipitation flux due to both ECH and whistler mode waves. A case study has been performed to calculate pitch angle diffusion coefficients using Gaussian function to represent wave energy distribution with frequency. It is found that, for electron energy <500 eV, the calculated diffusion coefficients using Gaussian function to represent ECH wave energy distribution are several orders of magnitude smaller or negligible as compared to diffusion coefficients calculated by temporal growth rates. However, the calculated pitch angle diffusion coefficients using Gaussian function for whistler mode wave energy distribution are in very good agreement with diffusion coefficients calculated by temporal growth rates. It is concluded that representing the ECH wave energy distribution with frequency by a Gaussian function grossly underestimates the low energy (<500 eV) electron precipitation flux due to ECH waves.
Stimulation of whistler activity by an artificial ground-based low frequency acoustic wave source
Soroka, Silvestr; Kim, Vitaly; Khegay, Valery; Kalita, Bogdan
This paper presents some results of an active experiment aimed to impact the ionosphere with low frequency acoustic waves artificially generated in the near-ground atmosphere. The main goal of the experiment was checking if the artificially generated acoustic waves could affect whistler occurrence at middle latitudes. As a source of acoustic waves we used twin powerful sonic speakers. One of which produced acoustic waves at a frequency of 600 Hz while the other one at a frequency of 624 Hz with intensity of 160 dB at a distance of 1 m away from end of the horn. The duration of sonic pulse was one minute. As a result of acoustic wave interference above the acoustic wave source there appears some kind of a virtual sonic antenna that radiates lower frequency acoustic waves at a frequency being equal to the difference of the two initially generated frequencies (624 Hz - 600 Hz = 24 Hz). The resulting acoustic wave is capable to penetrate to higher altitudes than the initially generated waves do because of its lower frequency. A whistler detector was located at about 100 m far away from the acoustic wave source. We performed the 50 experiments at Lviv (49.50° N, 24.00° E) with acoustic influence on the atmosphere-ionosphere system. The obtained results indicate that the emitted low frequency acoustic waves were clearly followed by enhanced whistler occurrence. We suggest that the observations could be interpreted how increase of transparency of ionosphere and upward refraction of VLF spherics resulted from modulation of local atmospheric parameters by the acoustic waves. These two effects produce to the increase of amount of the whistlers.
Rapid energization of radiation belt electrons by nonlinear wave trapping
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Y. Katoh
2008-11-01
Full Text Available We show that nonlinear wave trapping plays a significant role in both the generation of whistler-mode chorus emissions and the acceleration of radiation belt electrons to relativistic energies. We have performed particle simulations that successfully reproduce the generation of chorus emissions with rising tones. During this generation process we find that a fraction of resonant electrons are energized very efficiently by special forms of nonlinear wave trapping called relativistic turning acceleration (RTA and ultra-relativistic acceleration (URA. Particle energization by nonlinear wave trapping is a universal acceleration mechanism that can be effective in space and cosmic plasmas that contain a magnetic mirror geometry.
Generation of whistler waves by continuous HF heating of the upper ionosphere
Vartanyan, A.; Milikh, G. M.; Eliasson, B.; Najmi, A. C.; Parrot, M.; Papadopoulos, K.
2016-07-01
Broadband VLF waves in the frequency range 7-10 kkHz and 15-19 kHz, generated by F region CW HF ionospheric heating in the absence of electrojet currents, were detected by the DEMETER satellite overflying the High Frequency Active Auroral Research Program (HAARP) transmitter during HAARP/BRIOCHE campaigns. The VLF waves are in a frequency range corresponding to the F region lower lybrid (LH) frequency and its harmonic. This paper aims to show that the VLF observations are whistler waves generated by mode conversion of LH waves that were parametrically excited by HF-pump-plasma interaction at the upper hybrid layer. The paper discusses the basic physics and presents a model that conjectures (1) the VLF waves observed at the LH frequency are due to the interaction of the LH waves with meter-scale field-aligned striations—generating whistler waves near the LH frequency; and (2) the VLF waves at twice the LH frequency are due to the interaction of two counterpropagating LH waves—generating whistler waves near the LH frequency harmonic. The model is supported by numerical simulations that show good agreement with the observations. The (Detection of Electromagnetic Emissions Transmitted from Earthquake Regions results and model discussions are complemented by the Kodiak radar, ionograms, and stimulated electromagnetic emission observations.
Chang, C. L.; Lipatov, A. S.; Drobot, A. T.; Papadopoulos, K.; Satya-Narayana, P.
1994-01-01
The dynamic response of a magnetized collisionless plasma to an externally driven, finite size, sudden switch-on current source across the magnetic field has been studied using a two dimensional hybrid code. It was found that the predominant plasma response was the excitation of whistler waves and the formation of current closure by induced currents in the plasma. The results show that the current closure path consists of: (a) two antiparallel field-aligned current channels at the end of the imposed current sheet; and (b) a cross-field current region connecting these channels. The formation of the current closure path occured in the whistler timescale much shorter than that of MHD and the closure region expanded continuously in time. The current closure process was accompanied by significant energy loss due to whistler radiation.
Wilson, L. B., III; Cattell, C. A.; Kellogg, P. J.; Wygant, J. R.; Goetz, K.; Breneman, A.; Kersten, K.
2011-01-01
Wepresent resultsof a studyof the characteristicsof very large amplitude whistler mode waves inside the terrestrial magnetosphere at radial distances of less than 15 RE using waveform capture data from the Wind spacecraft. We observed 247 whistler mode waves with at least one electric field component (105/247 had !80 mV/m peak!to!peak amplitudes) and 66 whistler mode waves with at least one search coil magnetic field component (38/66 had !0.8 nT peak!to!peak amplitudes). Wave vectors determined from events with three magnetic field components indicate that 30/46 propagate within 20 of the ambient magnetic field, though some are more oblique (up to "50 ). No relationship was observed between wave normal angle and GSM latitude. 162/247 of the large amplitude whistler mode waves were observed during magnetically active periods (AE > 200 nT). 217 out of 247 total whistler mode waves examined were observed inside the radiation belts. We present a waveform capture with the largest whistler wave magnetic field amplitude (^8 nT peak!to!peak) ever reported in the radiation belts. The estimated Poynting flux magnitude associated with this wave is ^300 mW/m2, roughly four orders of magnitude above estimates from previous satellite measurements. Such large Poynting flux values are consistent with rapid energization of electrons.
Tenerani, A; Le Contel, O; Califano, F; Pegoraro, F; Robert, P; Cornilleau-Wehrlin, N; Sauvaud, J A
2012-10-12
We present a new model of self-consistent coupling between low frequency, ion-scale coherent structures with high frequency whistler waves in order to interpret Cluster data. The idea relies on the possibility of trapping whistler waves by inhomogeneous external fields where they can be spatially confined and propagate for times much longer than their characteristic electronic time scale. Here we take the example of a slow magnetosonic soliton acting as a wave guide in analogy with the ducting properties of an inhomogeneous plasma. The soliton is characterized by a magnetic dip and density hump that traps and advects high frequency waves over many ion times. The model represents a new possible way of explaining space measurements often detecting the presence of whistler waves in correspondence to magnetic depressions and density humps. This approach, here given by means of slow solitons, but more general than that, is alternative to the standard approach of considering whistler wave packets as associated with nonpropagating magnetic holes resulting from a mirror-type instability.
Whistler intensities above thunderstorms
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J. Fiser
2010-01-01
Full Text Available We report a study of penetration of the VLF electromagnetic waves induced by lightning to the ionosphere. We compare the fractional hop whistlers recorded by the ICE experiment onboard the DEMETER satellite with lightning detected by the EUCLID detection network. To identify the fractional hop whistlers, we have developed software for automatic detection of the fractional-hop whistlers in the VLF spectrograms. This software provides the detection times of the fractional hop whistlers and the average amplitudes of these whistlers. Matching the lightning and whistler data, we find the pairs of causative lightning and corresponding whistler. Processing data from ~200 DEMETER passes over the European region we obtain a map of mean amplitudes of whistler electric field as a function of latitudinal and longitudinal difference between the location of the causative lightning and satellite magnetic footprint. We find that mean whistler amplitude monotonically decreases with horizontal distance up to ~1000 km from the lightning source. At larger distances, the mean whistler amplitude usually merges into the background noise and the whistlers become undetectable. The maximum of whistler intensities is shifted from the satellite magnetic footprint ~1° owing to the oblique propagation. The average amplitude of whistlers increases with the lightning current. At nighttime (late evening, the average amplitude of whistlers is about three times higher than during the daytime (late morning for the same lightning current.
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2007-01-01
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Lightning on Venus inferred from whistler-mode waves in the ionosphere.
Russell, C T; Zhang, T L; Delva, M; Magnes, W; Strangeway, R J; Wei, H Y
2007-11-29
The occurrence of lightning in a planetary atmosphere enables chemical processes to take place that would not occur under standard temperatures and pressures. Although much evidence has been reported for lightning on Venus, some searches have been negative and the existence of lightning has remained controversial. A definitive detection would be the confirmation of electromagnetic, whistler-mode waves propagating from the atmosphere to the ionosphere. Here we report observations of Venus' ionosphere that reveal strong, circularly polarized, electromagnetic waves with frequencies near 100 Hz. The waves appear as bursts of radiation lasting 0.25 to 0.5 s, and have the expected properties of whistler-mode signals generated by lightning discharges in Venus' clouds.
Pitch angle scattering of diffuse auroral electrons by whistler mode waves
Energy Technology Data Exchange (ETDEWEB)
Villalon, E. [Northeastern Univ., Boston, MA (United States); Burke, W.J. [Hanscom Air Force Base, MA (United States)
1995-10-01
Resonant electron-whistler interactions in the plasma sheet are investigated as possible explanations of the nearly isotropic fluxes of low-energy electrons observed above the diffuse aurora. Whistler mode waves, propagating near the resonance cone with frequencies near or larger than half the equatorial electron cyclotron frequency, can interact with low-energy plasma sheet electrons. A Hamiltonian formulation is developed for test particles interacting with the coherent chorus emission spectra. The authors consider the second-order resonance condition which requires that inhomogeneities in the Earth`s magnetic field be compensated by a finite bandwidth of wave frequencies to maintain resonance for extended distances along field lines. These second-order interactions are very efficient in scattering the electrons toward the atmospheric loss cone. Numerical calculations are presented for the magnetic shell L=5.5 for wave amplitudes of {approximately}10{sup {minus}6} V/m, using different frequency and magnetospheric conditions. 34 refs., 7 figs.
Nonlinear wave-particle interactions in the outer radiation belts: Van Allen Probes results
Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton; Drake, James; Vasko, Ivan
2016-10-01
Huge numbers of different nonlinear structures (double layers, electron holes, non-linear whistlers, etc. referred to as Time Domain Structures - TDS) have been observed by the electric field experiment on board the Van Allen Probes. A large part of the observed non-linear structures are associated with whistler waves and some of them can be directly driven by whistlers. Observations of electron velocity distributions and chorus waves by the Van Allen Probe B provided long-lasting signatures of electron Landau resonant interactions with oblique chorus waves in the outer radiation belt. In the inhomogeneous geomagnetic field, such resonant interactions then lead to the formation of a plateau in the parallel (with respect to the geomagnetic field) velocity distribution due to trapping of electrons into the wave effective potential. The feedback from trapped particles provides steepening of parallel electric field and development of TDS seeded from initial whistler structure (well explained in terms of Particle-In-Cell model). The decoupling of the whistler wave and the nonlinear electrostatic component is shown in PIC simulation in the inhomogeneous magnetic field system and are observed by the Van Allen Probes in the radiation belts.
Whistler mode waves and the electron heat flux in the solar wind: Cluster observations
Lacombe, Catherine; Matteini, Lorenzo; Santolik, Ondrej; Cornilleau-Wehrlin, Nicole; Mangeney, Andre; de Conchy, Yvonne; Maksimovic, Milan
2014-01-01
The nature of the magnetic field fluctuations in the solar wind between the ion and electron scales is still under debate. Using the Cluster/STAFF instrument, we make a survey of the power spectral density and of the polarization of these fluctuations at frequencies $f\\in[1,400]$ Hz, during five years (2001-2005), when Cluster was in the free solar wind. In $\\sim 10\\%$ of the selected data, we observe narrow-band, right-handed, circularly polarized fluctuations, with wave vectors quasi-parallel to the mean magnetic field, superimposed on the spectrum of the permanent background turbulence. We interpret these coherent fluctuations as whistler mode waves. The life time of these waves varies between a few seconds and several hours. Here we present, for the first time, an analysis of long-lived whistler waves, i.e. lasting more than five minutes. We find several necessary (but not sufficient) conditions for the observation of whistler waves, mainly a low level of the background turbulence, a slow wind, a relative...
Horne, R. B.; Thorne, R. M.; Meredith, N. P.; Anderson, R. R.
2003-07-01
There are two main theories for the origin of diffuse auroral electron precipitation: precipitation by electrostatic ECH waves and precipitation by whistler mode waves. Here we analyze a case event where whistler mode hiss, chorus, and ECH waves are intensified during a weak substorm injection event to identify the source of particle precipitation. Examination of the particle data shows that there are three sources of free energy: a temperature anisotropy, a loss cone, and a pancake distribution. Instability analysis shows that the temperature anisotropy excites whistler mode hiss whereas both the temperature anisotropy and the pancake distribution contribute to the excitation of chorus. ECH waves are driven unstable by the loss cone. Wave propagation studies show that the path integrated gain of hiss and chorus is almost unaffected by changes in the depth of the loss cone, whereas ECH waves are very sensitive. Analysis of the changes in the resonant energy during propagation shows that the hiss resonates with electrons above a few keV while chorus resonates below a few hundred eV. As a result, neither hiss nor chorus are likely to cause significant electron precipitation from a few hundred eV to a few keV for this event. On the other hand, ECH waves resonate with electrons in the energy range between that for chorus and hiss. ECH waves can scatter electrons with pitch angles of up to 80° into the loss cone. We conclude that ECH waves are responsible for the formation of the pancake distribution and are probably the main component of diffuse auroral precipitation during this event. We suggest that substorm-injected electrons are responsible for the intensification of hiss and ECH waves and that rapid scattering of electrons by ECH waves forms the pancake distribution which then excites chorus. We also suggest that rapid pitch angle scattering by ECH waves could be responsible for double frequency banded chorus emissions.
Propagation of a whistler wave incident from above on the lower nighttime ionosphere
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P. Bespalov
2017-05-01
Full Text Available The problems of reflection and transmission of a whistler wave incident in the nighttime ionosphere from above are considered. Numerical solution of the wave equations for a typical condition of the lower ionosphere is found. The solution area comprises both the region of strong wave refraction and a sharp boundary of the nighttime ionosphere (∼ 100 km. The energy reflection coefficient and horizontal wave magnetic field on the ground surface are calculated. The results obtained are important for analysis of the extremely low-frequency and very low-frequency (ELF–VLF emission phenomena observed from both the satellites and the ground-based observatories.
Whistler mode waves and Hall fields detected by MMS during a dayside magnetopause crossing
Contel, O. Le; Retinò, A.; Breuillard, H.; Mirioni, L.; Robert, P.; Chasapis, A.; Lavraud, B.; Chust, T.; Rezeau, L.; Wilder, F. D.; Graham, D. B.; Argall, M. R.; Gershman, D. J.; Lindqvist, P.-A.; Khotyaintsev, Y. V.; Marklund, G.; Ergun, R. E.; Goodrich, K. A.; Burch, J. L.; Torbert, R. B.; Needell, J.; Chutter, M.; Rau, D.; Dors, I.; Russell, C. T.; Magnes, W.; Strangeway, R. J.; Bromund, K. R.; Leinweber, H. K.; Plaschke, F.; Fischer, D.; Anderson, B. J.; Le, G.; Moore, T. E.; Pollock, C. J.; Giles, B. L.; Dorelli, J. C.; Avanov, L.; Saito, Y.
2016-06-01
We present Magnetospheric Multiscale (MMS) mission measurements during a full magnetopause crossing associated with an enhanced southward ion flow. A quasi-steady magnetospheric whistler mode wave emission propagating toward the reconnection region with quasi-parallel and oblique wave angles is detected just before the opening of the magnetic field lines and the detection of escaping energetic electrons. Its source is likely the perpendicular temperature anisotropy of magnetospheric energetic electrons. In this region, perpendicular and parallel currents as well as the Hall electric field are calculated and found to be consistent with the decoupling of ions from the magnetic field and the crossing of a magnetospheric separatrix region. On the magnetosheath side, Hall electric fields are found smaller as the density is larger but still consistent with the decoupling of ions. Intense quasi-parallel whistler wave emissions are detected propagating both toward and away from the reconnection region in association with a perpendicular anisotropy of the high-energy part of the magnetosheath electron population and a strong perpendicular current, which suggests that in addition to the electron diffusion region, magnetosheath separatrices could be a source region for whistler waves.
Interaction of energetic electrons with dust whistler-mode waves in magnetospheric dusty plasmas
Jafari, S.
2016-04-01
In this Letter, a new conceptual approach has been presented to investigate the interaction of energetic electrons with dust whistler-mode waves in magnetospheric dusty (complex) plasmas. Dust whistler-mode waves generated in the presence of charged dust grains in the magnetized dusty plasma, can scatter the launched electrons into the loss-cone leading to precipitation into the upper atmosphere which is an important loss process in the radiation belts and provides a major source of energy for the diffuse and pulsating aurora. To study the scattered electrons and chaotic regions, a Hamiltonian model of the electron-dust wave interaction has been employed in the magnetospheric plasma by considering the launched electron beam self-fields. Numerical simulations indicate that an electron beam interacting with the whistler-mode wave can easily trigger chaos in the dust-free plasma, while in the presence of dust charged grains in the plasma, the chaotic regions are quenched to some extent in the magnetosphere. Consequently, the rate of scattered electrons into the loss-cone reduces for the regions that the dust grains are present.
Electron acceleration by whistler-mode waves around the magnetic null during 3D reconnection
Energy Technology Data Exchange (ETDEWEB)
Xiao Fuliang [School of Physics and Electronic Sciences, Changsha University of Science and Technology, Changsha, 410004 (China); Zong Qiugang; Pu Zuyin; He Jiansen; Wang Yongfu [School of Earth and Space Sciences, Peking University, Beijing 100871 (China); Su Zhenpeng; Zheng Huinan [CAS Key Laboratory for Basic Plasma Physics, School of Earth and Space Sciences, University of Science and Technology of China, Hefei (China); Cao Jinbin, E-mail: qgzong@pku.edu.c [State Key Laboratory of Space Weather, PO Box 8701, Beijing 100080 (China)
2010-05-15
The magnetic field configuration around a magnetic null pair and its associated electron behavior during 3D magnetic reconnection have recently been reported from in situ observations. Electrons are suggested to be temporarily trapped in the central reconnection region as indicated by an electron density peak observed near the magnetic null (He J-S et al 2008 Geophys. Res. Lett. 35 L14104). It is highly interesting that energetic electron beams of a few kiloelectronvolts are found to be related to the magnetic null structure. However, the acceleration mechanism is still not fully understood. In this paper, we show that strong whistler-mode electromagnetic waves are indeed found around the magnetic null. Further we propose a new electron acceleration scenario of trapped electrons near the magnetic null points driven by the whistler-mode waves, which is confirmed by numerical results. It is demonstrated that whistler waves can enhance the phase space density (PSD) of electrons for energies of approx2 keV by a factor of 100 at lower pitch angles very rapidly, typically within 2 s. The accelerated electrons may escape from the loss cone of the magnetic cusp mirrors around the magnetic null, leading to the observed energetic beams. (brief communication)
Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution
Institute of Scientific and Technical Information of China (English)
ZHOU Qing-Hua; JIANG Bin; SHI Xiang-Hua; LI Jun-Qiu
2009-01-01
The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type (KT) distribution. Numerical calculations are performed for a direct compar-ison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency (e.g., ω 0.1Ωe) due to a larger fractional num-ber of the resonant electrons ηrel (which controls the wave growth), while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Arel by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.
Near-equatorial pitch angle diffusion of energetic electrons by oblique whistler waves
Villalon, Elena; Burke, William J.
1991-06-01
The pitch angle scattering of trapped, energetic electrons by obliquely propagating whistler waves in the equatorial regions of the plasmasphere is investigated. Storm-injected electrons moving along field lines near the equator interact with electromagnetic waves whose frequencies are Doppler-shifted to some harmonic of the cyclotron frequency. The wave normals are distributed almost parallel to the geomagnetic field. Waves grow from the combined contributions of a large reservoir of energetic electrons that are driven into the loss cone by the highest-harmonic interactions permitted to them. Relativistic, quasi-linear theory is applied to obtain self-consistent equations describing the temporal evolution of waves and particles over time scales which are longer than the particle bounce time and group time delay of the waves. The equilibrium solutions and their stability are studied, considering the reflection of the waves by the ionsphere and the coupling of multiple harmonic resonances.
Statistical analysis of monochromatic whistler waves near the Moon detected by Kaguya
Directory of Open Access Journals (Sweden)
Y. Katoh
2011-05-01
Full Text Available Observations are presented of monochromatic whistler waves near the Moon detected by the Lunar Magnetometer (LMAG on board Kaguya. The waves were observed as narrowband magnetic fluctuations with frequencies close to 1 Hz, and were mostly left-hand polarized in the spacecraft frame. We performed a statistical analysis of the waves to identify the distributions of their intensity and occurrence. The results indicate that the waves were generated by the solar wind interaction with lunar crustal magnetic anomalies. The conditions for observation of the waves strongly depend on the solar zenith angle (SZA, and a high occurrence rate is recognized in the region of SZA between 40° to 90° with remarkable north-south and dawn-dusk asymmetries. We suggest that ion beams reflected by the lunar magnetic anomalies are a possible source of the waves.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Density fluctuation spectrum in whistler turbulence
Energy Technology Data Exchange (ETDEWEB)
Shaikh, Dastgeer, E-mail: dastgeer.shaikh@uah.ed [Department of Physics and Center for Space Plasma and Aeronomy Research, University of Alabama in Huntsville, Huntsville, Alabama 35899 (United States)
2010-05-31
We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k{sup -7/3} spectrum, where k is a characteristic wavenumber.
Breuillard, H.; Le Contel, O.; Retino, A.; Chasapis, A.; Chust, T.; Mirioni, L.; Graham, D. B.; Wilder, F. D.; Cohen, I.; Vaivads, A.; Khotyaintsev, Yu. V.; Lindqvist, P.-A.; Marklund, G. T.; Burch, J. L.; Torbert, R. B.; Ergun, R. E.; Goodrich, K. A.; Macri, J.; Needell, J.; Chutter, M.; Rau, D.; Dors, I.; Russell, C. T.; Magnes, W.; Strangeway, R. J.; Bromund, K. R.; Plaschke, F.; Fischer, D.; Leinweber, H. K.; Anderson, B. J.; Le, G.; Slavin, J. A.; Kepko, E. L.; Baumjohann, W.; Mauk, B.; Fuselier, S. A.; Nakamura, R.
2016-07-01
Dipolarization fronts (DFs), embedded in bursty bulk flows, play a crucial role in Earth's plasma sheet dynamics because the energy input from the solar wind is partly dissipated in their vicinity. This dissipation is in the form of strong low-frequency waves that can heat and accelerate energetic electrons up to the high-latitude plasma sheet. However, the dynamics of DF propagation and associated low-frequency waves in the magnetotail are still under debate due to instrumental limitations and spacecraft separation distances. In May 2015 the Magnetospheric Multiscale (MMS) mission was in a string-of-pearls configuration with an average intersatellite distance of 160 km, which allows us to study in detail the microphysics of DFs. Thus, in this letter we employ MMS data to investigate the properties of dipolarization fronts propagating earthward and associated whistler mode wave emissions. We show that the spatial dynamics of DFs are below the ion gyroradius scale in this region (˜500 km), which can modify the dynamics of ions in the vicinity of the DF (e.g., making their motion nonadiabatic). We also show that whistler wave dynamics have a temporal scale of the order of the ion gyroperiod (a few seconds), indicating that the perpendicular temperature anisotropy can vary on such time scales.
Directory of Open Access Journals (Sweden)
A. V. Artemyev
2013-04-01
Full Text Available The lifetimes of electrons trapped in Earth's radiation belts can be calculated from quasi-linear pitch-angle diffusion by whistler-mode waves, provided that their frequency spectrum is broad enough and/or their average amplitude is not too large. Extensive comparisons between improved analytical lifetime estimates and full numerical calculations have been performed in a broad parameter range representative of a large part of the magnetosphere from L ~ 2 to 6. The effects of observed very oblique whistler waves are taken into account in both numerical and analytical calculations. Analytical lifetimes (and pitch-angle diffusion coefficients are found to be in good agreement with full numerical calculations based on CRRES and Cluster hiss and lightning-generated wave measurements inside the plasmasphere and Cluster lower-band chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 5 MeV. Comparisons with lifetimes recently obtained from electron flux measurements on SAMPEX, SCATHA, SAC-C and DEMETER also show reasonable agreement.
Whistler Wave generation by an electron beam in a LAPTAG Plasma Physics experiment
Bridges, Gabriel; Pribyl, Patrick; Gekelman, Walter; Thomas, Sam; Birge-Lee, Henry; Wise, Joe; Katz, Cami; Baker, Bob; Marmie, Ken; Wolman, Ben; Buckley-Bonnano, Samuel
2015-11-01
A multi-grid pulsed electron beam (Ebeam = 1-4.8 KV, area =1.32 cm2, τ >5 μs) is inserted into a background plasma (He, n = 5X1010 cm3, B0z = 80 G, L = 1.5 m, dia = 40 cm). The pulsed electron beam power supply, can generate up to 4800 Volts at 10 Amps and was constructed by the LAPTAG high school students. The beam can be oriented at any angle with respect to the background magnetic field. The pulsed beam generates whistler waves by Cherenkov radiation. The waves are detected with 3 axis magnetic pickup probes which can be moved in planes transverse or parallel to the background magnetic field under computer control. The whistler wave pattern is used to determine the wavenumber k and Fourier analysis of the signal determines ω. The wave dispersion relation is compared to theory. Work done at BaPSF at UCLA and supported by NSF and DOE.
Unstable whistlers and Bernstein waves within the front of supercritical perpendicular shocks
Muschietti, Laurent; Lembege, Bertrand
2016-04-01
In supercritical shocks a significant fraction of ions is reflected at the steep shock ramp and carries a considerable amount of energy. The existence of reflected ions enables streaming instabilities to develop which are excited by the relative drifts between the populations of incoming ions, reflected ions, and electrons. The processes are fundamental to the transformation of directed kinetic energy into thermal energy, a tenet of shock physics. We model the particle distributions as a broad electron population and two ion populations, namely a core and a beam (representing the reflected ions) in order to investigate the kinetic instabilities possible under various wave propagation angles. Recently, assuming the ion beam is directed along the shock normal at 90° to the magnetic field Bo, we analyzed the linear dispersion properties by computing the full electromagnetic dielectric tensor [Muschietti and Lembege, AGU Fall meeting 2015]. Three types of waves were shown to be unstable: (1) Oblique whistlers with wavelengths about the ion inertia length which propagate toward upstream at angles about 50° to the magnetic field. Frequencies are a few times the lower-hybrid. The waves share many similarities to the obliquely propagating whistlers measured in detail by Polar [Hull et al., JGR 117, 2012]. (2) Quasi-perpendicular whistlers with wavelength covering a fraction of the electron inertia length which propagate toward downstream at angles larger than 80° to Bo. Frequencies are close to the lower-hybrid. (3) Bernstein waves with wavelengths close to the electron gyroradius which propagate toward upstream at angles within 5° of perpendicular to the magnetic field. Frequencies are close to the electron cyclotron. The waves have similarities to those reported by Wind and Stereo [Breneman et al., JGR 118, 2013; Wilson et al., JGR 115, 2010]. We will present electromagnetic 1D3V PIC simulations with predetermined propagation angles which illustrate the three types
Near-equatorial pitch angle diffusion of energetic electrons by oblique whistler waves
Energy Technology Data Exchange (ETDEWEB)
Villalon, E. (Northeastern Univ., Boston, MA (USA)); Burke, W.J. (Geophysics Lab., Hanscom AFB, MA (USA))
1991-06-01
The pitch angle scattering of trapped, energetic electrons by obliquely propagating whistler waves in the equatorial regions of the plasmasphere is investigated. Storm-injected electrons moving along field lines near the equator interact with electromagnetic waves whose frequencies are Doppler-shifted to some harmonic of the cyclotron frequency. The wave normals are distributed almost parallel to the geomagnetic field. Waves grow from the combined contributions of a large reservoir of energetic electrons that are driven into the loss cone by the highest-harmonic interactions permitted to them. Relativistic, quasi-linear theory is applied to obtain self-consistent equations describing the temporal evolution of waves and particles over time scales which are longer than the particle bounce time and group time delay of the waves. The equilibrium solutions and their stability are studied, considering the reflection of the waves by the ionosphere and the coupling of multiple harmonic resonances. The contributions of nonlocal wave sources are also included in the theory. Numerical computations based on the authors theoretical analysis for regions inside the plasmasphere (L{le}2) and near the plasmapause (L{approximately}4.5) and for the first three harmonic resonances are presented.
Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence
Galtier, S
2014-01-01
The role of magnetic helicity is investigated in kinetic Alfv\\'en wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0 {\\bf e_\\parallel}$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \\& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\\tilde n = -6$, where $n$ and $\\tilde n$ are the power law indices of the perpendicular (to ${\\bf b_0}$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\\tilde n = - 3.5$,...
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Observations of Quasi-Periodic Whistler Mode Waves by the Van Allen Probes
Hospodarsky, George; Wilkinson, Darrelle; Kurth, William; Kletzing, Craig; Santolik, Ondrej
2016-10-01
Observed in Earth's inner magnetosphere, quasi-periodic whistler mode emissions (QP) are electromagnetic waves in the frequency range from a few hundred Hz to a few kHz that exhibit a periodic modulation (typically a few minutes) of their wave intensity. These waves were first detected at high latitude ground stations, but more recently have been observed by a number of spacecraft, including the twin Van Allen Probes. The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument simultaneously measures the vector wave magnetic field and electric field, allowing wave propagation parameters, such as wave normal angle and Poynting vector, to be obtained. Almost four years of Van Allen Probes data have been examined and a statistical survey of the occurrence and properties of the QP emissions has been performed. The QP emissions were found to have periods ranging from 1 to 16 minutes with events lasting from less than 1 hour up to 6 hours. Some events were detected on successive orbits and a number of events were simultaneously detected by both spacecraft, even during large spacecraft separations, providing an opportunity to investigate the source and propagation properties of these waves.
Frequencies of wave packets of whistler-mode chorus inside its source region: a case study
Directory of Open Access Journals (Sweden)
O. Santolik
2008-06-01
Full Text Available Whistler-mode chorus is a structured wave emission observed in the Earth's magnetosphere in a frequency range from a few hundreds of Hz to several kHz. We investigate wave packets of chorus using high-resolution measurements recorded by the WBD instrument on board the four Cluster spacecraft. A night-side chorus event observed during geomagnetically disturbed conditions is analyzed. We identify lower and upper frequencies for a large number of individual chorus wave packets inside the chorus source region. We investigate how these observations are related to the central position of the chorus source which has been previously estimated from the Poynting flux measurements. We observe typical frequency bandwidths of chorus of approximately 10% of the local electron cyclotron frequency. Observed time scales are around 0.1 s for the individual wave packets. Our results indicate a lower occurrence probability for lower frequencies in the vicinity of the central position of the source compared to measurements recorded closer to the outer boundaries of the source. This is in agreement with recent research based on the backward wave oscillator theory.
Holzworth, R. H.; McCarthy, M. P.; Pfaff, R. F.; Jacobson, A. R.; Willcockson, W. L.; Rowland, D. E.
2011-01-01
Direct evidence is presented for a causal relationship between lightning and strong electric field transients inside equatorial ionospheric density depletions. In fact, these whistler mode plasma waves may be the dominant electric field signal within such depletions. Optical lightning data from the Communication/Navigation Outage Forecast System (C/NOFS) satellite and global lightning location information from the World Wide Lightning Location Network are presented as independent verification that these electric field transients are caused by lightning. The electric field instrument on C/NOFS routinely measures lightning ]related electric field wave packets or sferics, associated with simultaneous measurements of optical flashes at all altitudes encountered by the satellite (401.867 km). Lightning ]generated whistler waves have abundant access to the topside ionosphere, even close to the magnetic equator.
The mid-high latitude whistler mode chorus waves observed around substorm onsets
Institute of Scientific and Technical Information of China (English)
YANG JunYing; CAO JinBin; YAN ChunXiao; LI LiuYuan; MA YuDuan
2008-01-01
Using the data of LFEW/TC-2, we studied the dawn side chorus around substorm onsets during a strong geomagnetic storm in November 2004. During this storm, LFEW/TC-2 observed 14 dawnside chorus events. Nine of them were associated with substorms and occurred within 40 min around the substorm onsets. The fre-quencies of waves have a very good correlation with the half equatorial electron cyclotron frequencies. Chorus can be excited in the region near magnetic equato-rial plane and then propagate to the mid and high latitudes. When the wave fre-quencies reach the local lower hybrid frequencies, chorus can be reflected due to the lower hybrid resonance. The time delay between the chorus and its echo is about 28 min. Previous observations show that the chorus can propagate at most to the magnetic latitudes of 40°. LFEW/TC-2 found for the first time that the chorus in space could propagate to the magnetic latitude of 70°. Since most of the previous chorus observatlons are made close to the magnetic equatorial plane, our results are Important for the studies of excitation and propagation of whistler mode wave, and relevant relativistic electron acceleration in the magnetosphere.
Energy Estimates of Lightning-Generated Whistler-Mode Waves in the Venus Ionosphere
Hart, Richard; Russell, Christopher T.; Zhang, Tielong
2016-10-01
The dual fluxgate magnetometer on the Venus Express Mission sampled at 128 Hz allowing for signals up to 64 Hz to be detected. These signals are found at all local times and at altitudes up to 600 km while near periapsis. The spacecraft had a periapsis within 15 degrees of the north pole for nearly the entire mission, concentrating observations at high latitudes. At solar minimum, when the ionosphere can become strongly magnetized, the waves were more readily guided along the field up to the spacecraft. During this time, whistlers were observed 3% of the time while VEX was at 250 km altitude. Detection rates reached 5% at this altitude while near the dawn terminator due to a low altitude magnetic belt that provides a radial component enabling better access of the signals to the spacecraft.Since the majority of these observations were made at relatively low altitudes, reasonable assumptions can be made about the ionospheric conditions along the wave's path from the base of the ionosphere to the spacecraft. The electron density can be inferred by utilizing the VERA model and scaling it to match the solar cycle conditions during the Venus Express campaign. With the electron density and the three components of the magnetic field measurement, we then calculate the Poynting flux to determine the energy density of the wave. This enables us to determine the strength of the source lightning and compares this strength to that on Earth.
The mid-high latitude whistler mode chorus waves observed around substorm onsets
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using the data of LFEW/TC-2, we studied the dawn side chorus around substorm onsets during a strong geomagnetic storm in November 2004. During this storm, LFEW/TC-2 observed 14 dawnside chorus events. Nine of them were associated with substorms and occurred within 40 min around the substorm onsets. The fre-quencies of waves have a very good correlation with the half equatorial electron cyclotron frequencies. Chorus can be excited in the region near magnetic equato-rial plane and then propagate to the mid and high latitudes. When the wave fre-quencies reach the local lower hybrid frequencies, chorus can be reflected due to the lower hybrid resonance. The time delay between the chorus and its echo is about 28 min. Previous observations show that the chorus can propagate at most to the magnetic latitudes of 40°. LFEW/ TC-2 found for the first time that the chorus in space could propagate to the magnetic latitude of 70°. Since most of the previous chorus observations are made close to the magnetic equatorial plane, our results are important for the studies of excitation and propagation of whistler mode wave, and relevant relativistic electron acceleration in the magnetosphere.
Multi-Spacecraft Analysis of Plasma Jet Events and Associated Whistler-Wave Emissions using MMS Data
Breuillard, Hugo; Le Contel, Olivier; Retino, Alessandro; Chasapis, Alexandros; Chust, Thomas; Cohen, Ian; Wilder, Frederick; Graham, Daniel; Khotyaintsev, Yuri
2016-04-01
Plasma jets aka bursty bulk flows play a crucial role in Earth's plasmasheet dynamics, in particular during substorms where they can sometimes even penetrate down to the geosynchronous orbit. The energy input from the solar wind is partly dissipated in jet fronts(also called dipolarization fronts) in the form of strong whistler waves that can heat and accelerate energetic electrons. The ratio of the energy transported during jets to the substorm energy consumption is still under debate due to instrumental limitations. In May 2015 the Magnetospheric Multiscale (MMS) mission evolves in a string-of-pearls configuration with an average inter-satellite distance of 300 km which allows us to study in detail the microphysics of these phenomena. Thus in this study we employ MMS data to investigate the properties of jet fronts propagating earthward and their associated whistler-mode wave emissions. We show that the spatial dynamics of jet fronts are of the order of the ion gyroradius and whistler-wave dynamics have a temporal scale of a few seconds. We also investigate the energy dissipation associated with such waves and their interaction with energetic electrons in the vicinity of the flow/jet braking region. In addition, we make use of ray tracing simulations to evaluate their propagation properties, as well as their impact on particles in the off-equatorial magnetosphere.
Energy Technology Data Exchange (ETDEWEB)
Kudrin, Alexander V.; Shkokova, Natalya M. [Department of Radiophysics, University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950 (Russian Federation); Ferencz, Orsolya E. [MTA Research Centre for Astronomy and Earth Sciences, Csatkai E. u. 6–8, Sopron H-9400 (Hungary); Zaboronkova, Tatyana M. [Department of Radiophysics, University of Nizhny Novgorod, 23 Gagarin Ave., Nizhny Novgorod 603950 (Russian Federation); Department of Nuclear Physics, R. E. Alekseev State Technical University of Nizhny Novgorod, 24 Minin St., Nizhny Novgorod 603950 (Russian Federation)
2014-11-15
Pulsed radiation from a loop antenna located in a cylindrical duct with enhanced plasma density is studied. The radiated energy and its distribution over the spatial and frequency spectra of the excited waves are derived and analyzed as functions of the antenna and duct parameters. Numerical results referring to the case where the frequency spectrum of the antenna current is concentrated in the whistler range are reported. It is shown that under ionospheric conditions, the presence of an artificial duct with enhanced density can lead to a significant increase in the energy radiated from a pulsed loop antenna compared with the case where the same source is immersed in the surrounding uniform magnetoplasma. The results obtained can be useful in planning active ionospheric experiments with pulsed electromagnetic sources operated in the presence of artificial field-aligned plasma density irregularities that are capable of guiding whistler waves.
Whistler damping at oblique propagation - Laminar shock precursors
Gary, S. P.; Mellott, M. M.
1985-01-01
This paper addresses the collisionless damping of whistlers observed as precursors standing upstream of oblique, low-Mach number terrestrial bow shocks. The linear theory of electromagnetic waves in a homogeneous Vlasov plasma with Maxwellian distribution functions and a magnetic field is considered. Numerical solutions of the full dispersion equation are presented for whistlers propagating at an arbitrary angle with respect to the magnetic field. It is demonstrated that electron Landau damping attenuates oblique whistlers and that the parameter which determines this damping is beta-e. In a well-defined range of parameters, this theory provides damping lengths which are the same order of magnitude as those observed. Thus electron Landau damping is a plausible process in the dissipation of upstream whistlers. Nonlinear plasma processes which may contribute to precursor damping are also discussed, and criteria for distinguishing among these are described.
Highly resolved effects of whistler-mode hiss waves in March 2013
Ripoll, J. F.; Santolik, O.; Reeves, G. D.; Kurth, W. S.; Kletzing, C.
2015-12-01
We present a simulation of effects of whistler-mode waves on radiation belt electrons for the entire month of March 2013. Frequency dependent wave intensities as well as ambient plasma density are obtained from the EMFISIS Waves instrument onboard the Van Allen Probes using fine temporal (8 hours) and spatial (0.1L) resolutions. Pitch angle diffusion that produces electron scattering is computed using the Lyons et al. [1972] model, from L=1.8 to L=5.5 and energy in [0.05, 6] MeV. Electron lifetimes are deduced from the steady state of electron pitch angle diffusion. Such a computation requires 4000 thousands processors during 10 hours. It leads to a fine description of the hiss effects in the plasmasphere and in its exterior neighborhood. Losses follow a complex and dynamic filamentary structure, imposed by the wave properties (mainly frequency and amplitude), that sculpts the slot as such. Their daily structure in the (E-L) plane is characteristic [Lyons & Thorne, 1973], dynamic, and similar to recent slot observations from the Van Allen probes [Reeves et al., 2015]. Low energy electrons are less influenced by intense hiss scattering below L=4, which favors their travel down to the vicinity of the Earth, explaining thus the existence of a wide inner belt. On the other hand MeV electrons evolve in a more hostile environment that will depopulate them as they migrate from L~5 down to L~2.5. Ultra-relativistic electrons are not sensible to hiss waves before two and three Earth radii.
Xiao, Fuliang; Zong, Qiugang; Pu, Zuyin; Su, Zhenpeng; Cao, Jinbin; He, Jiansen; Wang, Yongfu; Zheng, Huinan
2010-05-01
The magnetic field configuration around a magnetic null pair and its associated electron behavior during 3D magnetic reconnection have recently been reported from in situ observations. Electrons are suggested to be temporarily trapped in the central reconnection region as indicated by an electron density peak observed near the magnetic null (He J-S et al 2008 Geophys. Res. Lett. 35 L14104). It is highly interesting that energetic electron beams of a few kiloelectronvolts are found to be related to the magnetic null structure. However, the acceleration mechanism is still not fully understood. In this paper, we show that strong whistler-mode electromagnetic waves are indeed found around the magnetic null. Further we propose a new electron acceleration scenario of trapped electrons near the magnetic null points driven by the whistler-mode waves, which is confirmed by numerical results. It is demonstrated that whistler waves can enhance the phase space density (PSD) of electrons for energies of ~2 keV by a factor of 100 at lower pitch angles very rapidly, typically within 2 s. The accelerated electrons may escape from the loss cone of the magnetic cusp mirrors around the magnetic null, leading to the observed energetic beams.
On the dispersion law of low-frequency electron whistler waves in a multi-ion plasma
Directory of Open Access Journals (Sweden)
B. V. Lundin
2008-06-01
Full Text Available A new and simple dispersion law for extra-low-frequency electron whistler waves in a multi-ion plasma is derived. It is valid in a plasma with finite ratio ω_{c}/ω_{pe} of electron gyro-to-plasma frequency and is suitable for wave frequencies much less than ω_{pe} but well above the gyrofrequencies of most heavy ions. The resultant contribution of the ions to the dispersion law is expressed by means of the lower hybrid resonance frequency, the highest ion cutoff frequency and the relative content of the lightest ion. In a frequency domain well above the ions' gyrofrequencies, this new dispersion law merges with the "modified electron whistler dispersion law" determined in previous works by the authors. It is shown that it fits well to the total cold plasma electron whistler dispersion law, for different orientations of the wave vectors and different ion constituents, including negative ions or negatively charged dust grains.
Resonance between coherent whistler mode waves and electrons in the topside ionosphere
Neubert, T.; Bell, T. F.; Storey, L. R. O.
1987-01-01
Landau resonance and cyclotron resonance of coherent whistler mode waves and energetic electrons are explored for magnetoplasmas with appreciable gradients in the plasma density and magnetic field strength. It is shown that in the topside ionosphere of the earth near the ion transition height the gradients in plasma density and magnetic field strength along a magnetic field line may match in a way which enhances both Landau and cyclotron interactions between waves and electrons at the loss cone pitch angle. The pitch angle scattering induced by a signal from a ground-based VLF transmitter in the ionosphere above the transmitter has been estimated and compared to the pitch angle scattering induced by naturally occurring ELF hiss through cyclotron resonance. It is found that the expected scattering due to plasmapheric hiss is an order of magnitude larger than that due to Landau resonance in the topside ionosphere. Pitch angle scattering due to cyclotron resonance in the topside ionosphere, however, may be larger by a factor of 2. It is suggested that the 'fast Trimpi' effect may be caused by a cyclotron resonance interaction in the topside ionosphere.
Whistler-mode phenomena in electron MHD plasmas
Stenzel, R. L.
2003-12-01
While the linear properties of plane whistler waves are well known, many new phenomena of bounded wavepackets and nonlinear effects are worth to describe. The present talk will review laboratory observations of whistler filaments, whistler vortices, whistler wings, whistler-sound modes in high-beta plasmas, nonlinear whistlers forming magnetic null points, and magnetic reconnection in EMHD plasmas. The time-varying magnetic field of a spatially bounded whistler wave packet consists of 3-D vortices. Each vortex can be decomposed into linked toroidal and poloidal field components. The self-helicity is positive for propagation along the field, negative for opposite propagation. Helicity injection from a suitable source produces unidirectional propagation. Magnetic helicity changes sign, i.e., is not conserved, when the propagation direction along B changes, for example due to reflection or propagation through a magnetic null point. In ideal EMHD the electric and magnetic forces on the electrons are equal, -n e E +J x B=0, i.e., the electron fluid is not compressed. Force-free vortices do not interact during collisions. Vortices are excited with pulsed magnetic antennas or pulsed electrodes. Both transient currents and fields can form vortices that propagate in the whistler mode. Moving dc magnets or dc current systems can also induce whistler modes in a magnetized plasma. These form a Cherenkov-like radiation pattern, a ``whistler wing.'' Nonlinear phenomena arise from wave-induced modifications of the electron temperature, density and magnetic field. In collisional plasmas electrons are heated by strong whistlers. Modifications of the classical conductivity leads to current filamentation. On a slower time scale density modifications arise from ambipolar fields associated with electron heating. In a filamentation instability a strong whistler wave is ducted along a narrow field-aligned density depression. The ion density is also modified by the ac electric field of
Erokhin, N S; Rycroft, M J; Nunn, D G
1996-01-01
The influence of wave frequency variation on the anomalous cyclotron resonance $\\omega=\\omega_{Be}+kv_{\\|}$ interaction (ACRI) of energetic electrons with a ducted finite amplitude whistler-mode wave propagating through the so-called transient plasma layer (TPL) in the magnetosphere or in the ionosphere is studied both analytically and numerically. The anomalous cyclotron resonance interaction takes place in the case when the whistler-mode wave amplitude $B_{W}$ is consistent with the gradient of magnetic field interacting energetic electrons (synchronous particles) is determined. The efficiencies of both the pitch-angle scattering of resonant electrons and their transverse acceleration are studied and the efficiencies dependence on the magnitude and sign of the wave frequency drift is considered. It has been shown that in the case of ACRI occuring under conditions relevant to VLF-emission in the magnetosphere, the energy and pitch-angle changes of synchronous electrons may be enchanced by a factor $10^2 \\div...
Kuzichev, Ilya; Shklyar, David
2016-04-01
One of the most challenging problems of the radiation belt studies is the problem of particles energization. Being related to the process of particle precipitation and posing a threat to scientific instruments on satellites, the problem of highly energetic particles in the radiation belts turns out to be very important. A lot of progress has been made in this field, but still some aspects of the energization process remain open. The main mechanism of particle energization in the radiation belts is the resonant interaction with different waves, mainly, in whistler frequency range. The problem of special interest is the resonant wave-particle interaction of the electrons of relativistic energies. Relativistic resonance condition provides some important features such as the so-called relativistic turning acceleration discovered by Omura et al. [1, 2]. This process appears to be a very efficient mechanism of acceleration in the case of interaction with the whistler-mode waves propagating along geomagnetic field lines. But some whistler-mode waves propagate obliquely to the magnetic field lines, and the efficiency of relativistic turning acceleration in this case is to be studied. In this report, we present the Hamiltonian theory of the resonant interaction of relativistic electrons with oblique monochromatic whistler-mode waves. We have shown that the presence of turning point requires a special treatment when one aims to derive the resonant Hamiltonian, and we have obtained two different resonant Hamiltonians: one to be applied far enough from the turning point, while another is valid in the vicinity of the turning point. We have performed numerical simulation of relativistic electron interaction with whistler-mode waves generated in the ionosphere by a monochromatic source. It could be, for example, a low-frequency transmitter. The wave-field distribution along unperturbed particle trajectory is calculated by means of geometrical optics. We show that the obliquity of
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A.; Neishtadt, A. I. [Space Research Institute, RAS, Moscow, Russia, 117997 (Russian Federation); Mourenas, D.; Krasnoselskikh, V. [LPC2E/CNRS—University of Orleans, 3A, Avenue de la Recherche Scientifique, F-45071 Orleans Cedex (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-11-15
We investigate electron trapping by high-amplitude whistler-mode waves propagating at small as well as large angles relative to geomagnetic field lines. The inhomogeneity of the background magnetic field can result in an effective acceleration of trapped particles. Here, we derive useful analytical expressions for the probability of electron trapping by both parallel and oblique waves, paving the way for a full analytical description of trapping effects on the particle distribution. Numerical integrations of particle trajectories allow to demonstrate the accuracy of the derived analytical estimates. For realistic wave amplitudes, the levels of probabilities of trapping are generally comparable for oblique and parallel waves, but they turn out to be most efficient over complementary energy ranges. Trapping acceleration of <100 keV electrons is mainly provided by oblique waves, while parallel waves are responsible for the trapping acceleration of >100 keV electrons.
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Radiation Belt Electron Dynamics Driven by Large-Amplitude Whistlers
Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.
2013-01-01
Acceleration of radiation belt electrons driven by oblique large-amplitude whistler waves is studied. We show analytically and numerically that this is a stochastic process; the intensity of which depends on the wave power modified by Bessel functions. The type of this dependence is determined by the character of the nonlinear interaction due to coupling between action and phase. The results show that physically significant quantities have a relatively weak dependence on the wave power.
Teste, Alexandra; Parks, George K
2009-02-20
Relevant new clues to wave-particle interactions have been obtained in Earth's plasma sheet (PS). The plasma measurements made on Cluster spacecraft show that broadband (approximately 2-6 kHz) electrostatic emissions, in the PS boundary layer, are associated with cold counterstreaming electrons flowing at 5-12x10(3) km s(-1) through hot Maxwellian plasma. In the current sheet (CS), electromagnetic whistler mode waves (approximately 10-80 Hz) and compressional Alfvén waves (whistler mode emissions triggered by the cyclotron resonance instability.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
Kudrin, Alexander V.; Ostafiychuk, Oleg M.; Zaboronkova, Tatyana M.
2017-08-01
Whistler wave radiation from a loop antenna located in a cylindrical duct with enhanced plasma density is considered in the case where the wave frequency is less than the lower hybrid frequency. Using the full-wave formulation, the total radiation resistance and the partial radiation resistances corresponding to guided eigenmodes of such a duct and unguided waves radiating to the background magnetoplasma are calculated and analyzed as functions of the plasma and source parameters. The emphasis is placed on the radiation characteristics of the considered source in the presence of an artificial near-antenna duct that can be created during active experiments in the ionosphere. Conditions are revealed under which the total radiation resistance is predominantly determined by the excitation of the eigenmodes of the duct. It is shown that the presence of an enhanced density duct can lead to a notable increase in the radiation resistance of a loop antenna in the discussed frequency range even if the duct is rather narrow and capable of guiding only a single low-order eigenmode. The results obtained can be helpful in understanding the basic features of excitation of the ducted whistlers and planning the related ionospheric and laboratory experiments.
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
Fast dropouts of multi-MeV electrons due to combined effects of EMIC and whistler mode waves
Mourenas, D.; Artemyev, A. V.; Ma, Q.; Agapitov, O. V.; Li, W.
2016-05-01
We investigate how whole populations of 2-6 MeV electrons can be quickly lost from the Earth's outer radiation belt at L= 3-6 through precipitation into the atmosphere due to quasi-linear pitch angle scattering by combined electromagnetic ion cyclotron (EMIC) and whistler mode waves of realistic intensities occurring at the same or different local times. We provide analytical estimates of the corresponding relativistic electron lifetimes, emphasizing that the combined effects of both waves can lead to very fast (2-10 h) dropouts. Scaling laws for the loss timescales are derived, allowing us to determine the various plasma and wave parameter domains potentially leading to strong and fast dropouts. The analysis reveals that the fastest MeV electron dropouts occur at approximately the same rate over some high energy range and almost independently of EMIC wave amplitudes above a certain threshold. These results should help to better understand the dynamic variability of the radiation belts.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Whistler Mode Waves Excited by Electron Temperature Anisotropy%温度各向异性的电子激发的哨声波
Institute of Scientific and Technical Information of China (English)
赵波; 郭俊
2011-01-01
Adopting one dimensional particle-in-cell (PIC) simulations, we present a study on the evolution of the electron whistler waves driven by electron temperature ani-sotropy. Simulating results show that the electron temperature anisotropy can excite the whistler waves. If the ratio of electron plasma frequency to cyclotron frequency is large enough, the electron temperature anisotropy will drop rapidly which lead to the amplitude of whistler waves becomes very large. And also the frequency and wave number of the dominant whistler waves become smaller than those in the case with a smaller ratio. Especially, the effect of electrostatic waves become less important.%采用一维粒子模拟程序研究了由温度各向异性的电子激发的哨声波.结果表明,当电子等离子体频率和电子回旋频率的比值足够大的时候,和比值较小的情况相比:电子的垂直温度和平行温度的比值将会下降的很快；哨声波的强度迅速增强；哨声波的主频率及其对应的波数将会变小,静电波的影响急剧削弱.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Full-wave model of D-region upward VLF coupling to whistlers in the plasmasphere
Jacobson, A. R.; Shao, X.; Lay, E. H.
2012-12-01
Atmospheric-lightning-to-plasmasphere VLF coupling via whistlers is key to understanding the problem of radiation-belt losses and the slot region. In the lowermost ionosphere, the "D-region" (roughly 60 - 100 km altitude), the coupling occurs between the VLF incident from the "vacuum" below, to the electron whistler capable of transiting upward through the E- and F-regions above. We have modified our successful and data-validated D-region VLF downward-reflection model to predict upward-coupled whistler waveforms recorded on topside satellites. The model has been run in production mode for predicting downward-reflected waveforms recorded at ground stations, but the model's internal calculation also fully describes the "penetrating" solution that merges into the oblique electron whistler. We have begun to test the model against VLF, three-dimensional electric-field recordings from the Vector Electric Field Instrument (VEFI) [Pfaff et al., 2010] on the C/NOFS satellite. VEFI's broadband recording and large on-board memory serendipitously provide an excellent platform for studying lightning whistlers in the plasmasphere. We have already demonstrated [Jacobson et al., 2011] that VEFI is superbly suited for testing transionospheric propagation, in conjunction with the World Wide Lightning Location Network (WWLLN; see www.wwlln.net) to provide groundtruth location/time of the lightning strokes. This poster will describe latest results. Jacobson, A. R., R. H. Holzworth, R. F. Pfaff, and M. P. McCarthy (2011), Study of oblique whistlers in the low-latitude ionosphere, jointly with the C/NOFS satellite and the World-Wide Lightning Location Network, Annales Geophysicae, 29, 851-863. Pfaff, R., D. Rowland, H. Freudenreich, K. Bromund, K. Le, M. Acuna, J. Klenzing, C. Liebrecht, S. Martin, W. J. Burke, N. C. Maynard, D. E. Hunton, P. A. Roddy, J. O. Ballenthin, and G. R. Wilson (2010), Observations of DC electric fields in the low-latitude ionosphere and their variations with
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
Modulational instability of plasma waves in two dimensions
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul
1996-01-01
The nonlinear behavior of whistler waves coupled to either fast magnetosonic waves (FMS) or slow magnetosonic waves (SMS) is investigated in two spatial dimensions. For each branch our investigation is based on a numerical solution of a reduced set of equations consisting of two partial...... differential equations, of which one, describing the evolution of the whistler wave envelope, is complex of first order in time and the other, describing the slow response of the medium in which the whistler wave is propagating, is real and of second order in time. These equations were solved in a two...... of nonlinear waves in dispersive media....
Pritchett, P. L.; Schriver, D.; Ashour-Abdalla, M.
1991-01-01
A one-dimensional electromagnetic particle simulation model is constructed to study the excitation of whistler waves in the presence of a cold plasma cloud for conditions representative of those after the release of lithium in the inner plasma sheet during the Combined Release and Radiation Effect Satellite mission. The results indicate that a standing-wave pattern with discrete wave frequencies is formed within the cloud. The magnetic wave amplitude inside the cloud, which is limited by quasi-linear diffusion, is of the order of several nanoteslas. Assuming a magnetospheric loss cone of 5 deg, the observed pitch angle diffusion produced by the whistler waves is sufficient to put the electrons on strong diffusion.
Shklyar, D. R.
2017-01-01
We study the problem of energy exchange between waves and particles, which leads to energization of the latter, in an unstable plasma typical of the radiation belts. The ongoing Van Allen Probes space mission brought this problem among the most discussed in space physics. A free energy which is present in an unstable plasma provides the indispensable condition for energy transfer from lower energy particles to higher-energy particles via resonant wave-particle interaction. This process is studied in detail by the example of electron interactions with whistler mode wave packets originated from lightning-induced emission. We emphasize that in an unstable plasma, the energy source for electron energization is the energy of other particles, rather than the wave energy as is often assumed. The way by which the energy is transferred from lower energy to higher-energy particles includes two processes that operate concurrently, in the same space-time domain, or sequentially, in different space-time domains, in which a given wave packet is located. In the first process, one group of resonant particles gives the energy to the wave. The second process consists in wave absorption by another group of resonant particles, whose energy therefore increases. We argue that this mechanism represents an efficient means of electron energization in the radiation belts.
Exact solitary wave solutions of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Perpendicular ion acceleration in whistler turbulence
Energy Technology Data Exchange (ETDEWEB)
Saito, S. [Graduate School of Science, Nagoya University, Furocho, Chikusa, Nagoya 464-8601 (Japan); Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190, Toyama 930-8555 (Japan)
2014-04-15
Whistler turbulence is an important contributor to solar wind turbulence dissipation. This turbulence contains obliquely propagating whistler waves at electron scales, and these waves have electrostatic components perpendicular to the mean magnetic field. In this paper, a full kinetic, two-dimensional particle-in-cell simulation shows that whistler turbulence can accelerate ions in the direction perpendicular to the mean magnetic field. When the ions pass through wave-particle resonances region in the phase space during their cyclotron motion, the ions are effectively accelerated in the perpendicular direction. The simulation results suggest that whistler turbulence contributes to the perpendicular heating of ions observed in the solar wind.
Coherent whistler emissions in the magnetosphere – Cluster observations
Directory of Open Access Journals (Sweden)
I. Dandouras
2007-02-01
Full Text Available The STAFF-SC observations complemented by the data from other instruments on Cluster spacecraft were used to study the main properties of magnetospheric lion roars: sporadic bursts of whistler emissions at f~0.1–0.2fe where fe is the electron gyrofrequency. Magnetospheric lion roars are shown to be similar to the emissions in the magnetosheath while the conditions for their generation are much less favorable: the growth rate of the cyclotron temperature anisotropy instability is much smaller due to a smaller number of the resonant electrons. This implies a nonlinear mechanism of generation of the observed wave emissions. It is shown that the observed whistler turbulence, in reality, consists of many nearly monochromatic wave packets. It is suggested that these structures are nonlinear Gendrin's whistler solitary waves. Properties of these waves are widely discussed. Since the group velocity of Gendrin's waves is aligned with the magnetic field, these well guided wave packets can propagate through many magnetic "bottles" associated with mirror structures, without being trapped.
Yoon, Young Dae; Bellan, Paul M.
2016-10-01
A full three-dimensional computer code was developed in order to simulate a 3D-localized magnetic reconnection. We assume an incompressible two-fluid regime where the ions are stationary, and electron inertia and Hall effects are present. We solve a single dimensionless differential equation for perturbed magnetic fields with arbitrary background fields. The code has successfully reproduced both experimental and analytic solutions to resonance and Gendrin mode whistler waves in a uniform background field. The code was then modified to model 3D-localized magnetic reconnection as a 3D-localized perturbation on a hyperbolic-tangent background field. Three-dimensional properties that are asymmetric in the out-of-plane direction have been observed. These properties pertained to magnetic field lines, electron currents and their convection. Helicity and energy have also been examined, as well as the addition of a guide field.
Sahraoui, Fouad; Goldstein, Melvyn L.
2010-01-01
Over the past few decades, large-scales solar wind (SW) turbulence has been studied extensively, both theoretically and observationally. Observed power spectra of the low frequency turbulence, which can be described in the magnetohydrodynamic (MHD) limit, are shown to obey the Kolmogorov scaling, $k"{ -5/3 }$, down the local proton gyrofrequency ($C{ci} \\sim O.l$-Hz). Turbulence at frequencies above $C{ci}$ has not been thoroughly investigated and remains far less well understood. Above $C{ ci}$ the spectrum steepens to $\\sim f"{ -2.5}$ and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfven waves (KA W) or by whistler waves, before it is dissipated at small scales, In a case study Sahraoui et al., PRL (2009) have reported the first direct determination of the dissipation range of solar wind turbulence near the electron gyroscale using the high resolution Cluster magnetic and electric field data (up to $10"2$-Hz in the spacecraft reference frame). Above the Doppler-shifted proton scale $C{\\rho i}$ a new inertial range with a scaling $\\sim f"{ -2.3}$ has been evidenced and shown to remarkably agree with theoretical predictions of a quasi-two-dimensional cascade into KA W turbulence. Here, we use a wider sample of data sets of small scale SW turbulence under different plasma conditions, and investigate under which physical criteria the KA W (or the whistler) turbulence may be observed to carry out the cascade at small scales, These new observations/criteria are compared to the predictions on the cascade and the (kinetic) dissipation from the Vlasov theory. Implications of the results on the heating problem of the solar wind will be discussed.
New results of investigations of whistler-mode chorus emissions
Directory of Open Access Journals (Sweden)
O. Santolík
2008-07-01
Full Text Available This review summarizes selected recent results obtained during investigation of whistler-mode chorus emissions in the Earth's magnetosphere. Special attention is paid to results published during the last five years, with a focus on the results of the CLUSTER project. The nonlinear nature of chorus emissions is demonstrated using both theoretical results and measurements. Selected areas of research on whistler-mode chorus are covered and the paper especially reports new results on substructure and amplitudes of chorus wave packets, on new observations of frequency differences of chorus wave packets at different points in space and on their possible interpretations, on results concerning determination of position and size of the source region of chorus, on recent observational and theoretical results which lead to improved description of propagation of chorus from its source, and, finally, on comparison of chorus measurements with corresponding values deduced from nonlinear theory and simulations.
Transition to whistler mediated magnetic reconnection
Mandt, M. E.; Denton, R. E.; Drake, J. F.
1994-01-01
The transition in the magnetic reconnection rate from the resistive magnetohydrodynamic (MHD) regime where the Alfen wave controls reconnection to a regime in which the ions become unmagnetized and the whistler wave mediates reconnection is explored with 2-D hybrid simulations. In the whistler regime the electrons carry the currents while the ions provide a neutralizing background. A simple physical picture is presented illustrating the role of the whistler mediated reconnection is calculated analytically. The development of an out-of-plane component of the magnetic field is an observable signature of whistler driven reconnection.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Pandey, R. S.; Kaur, Rajbir
2016-10-01
In present paper, field aligned whistler mode waves are analyzed, in the presence of DC field in background plasma having relativistic distribution function in the magnetosphere of Uranus. The work has been examined for relativistic Maxwellian and loss-cone distribution function. In both the cases, we have studied the effect of various plasma parameters on the growth rate of waves by using the method of characteristics and discussed using data provided by Voyager 2. Growth rate has increased by increasing the magnitude of electric field, temperature anisotropy, energy density and number density of particles for Maxwellian and loss-cone background. However, when relativistic factor (λ =√{ 1 -v2 /c2 }) increases, growth rate decreases. The significant increase in real frequency of whistler waves can be observed. The results can be used for comparative study of planetary magnetospheres. The derivation can also be adapted to study various other instabilities in magnetosphere of Uranus.
Numerical simulation of whistler-triggered VLF emissions observed in Antartica
Energy Technology Data Exchange (ETDEWEB)
Nunn, D. [Southhampton Univ., Southhampton (United Kingdom); Smith, A.J. [British Antarctic Survey, Cambridge (United Kingdom)
1996-03-01
The authors have extracted from VLF databases from British Antarctica Survey data taken at Halley and Faraday stations, examples of whistler-triggered emissions (WTE). The WTE are relatively narrow band emissions triggered by natural background whistlers undergoing nonlinear wave particle interactions generally in the equatorial regions. They occur with either rising or falling frequency relative to the triggering waves. Using a Vlasov type code the authors are able to simulate the types of emissions which are observed. 24 refs., 8 figs., 3 tabs.
Ambipolar transport via trapped-electron whistler instability along open magnetic field lines.
Guo, Zehua; Tang, Xian-Zhu
2012-09-28
An open field line plasma is bounded by a chamber wall which intercepts the magnetic field. Steady state requires an upstream plasma source balancing the particle loss to the boundary. In cases where the electrons have a long mean free path, ambipolarity in parallel transport critically depends on collisionless detrapping of the electrons via wave-particle interaction. The trapped-electron whistler instability, whose nonlinear saturation produces a spectrum of whistler waves that is responsible for the electron detrapping flux, is shown to be an unusually robust kinetic instability, which is essential to the universality of the ambipolar constraint in plasma transport.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed.......Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
Decrease of VLF transmitter signal and Chorus-whistler waves before l'Aquila earthquake occurrence
Directory of Open Access Journals (Sweden)
M. Y. Boudjada
2010-07-01
Full Text Available We investigate the VLF emissions observed by the Instrument Champ Electrique (ICE experiment onboard the DEMETER micro-satellite. We analyze intensity level variation 10 days before and after the occurrence of l'Aquila earthquake (EQ. We found a clear decrease of the VLF received signal related to ionospheric whistler mode (mainly Chorus emission and to signal transmitted by the DFY VLF station in Germany, few days (more than one week before the earthquake. The VLF power spectral density decreases of more than two orders of magnitude until the EQ, and it recovers to normal levels just after the EQ occurrence. The geomagnetic activity is principally weak four days before EQ and increases again one day before l'Aquila seismic event. Our results are discussed in the frame of short- and long-terms earthquakes prediction focusing on the crucial role of the magnetic field of the Earth.
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
Breneman, A.; Cattell, C.; Wygant, J.; Kersten, K.; Wilson, L. B., III; Schreiner, S.; Kellogg, P. J.; Goetz, K.
2011-01-01
We report observations of very large amplitude whistler mode waves in the Earth fs nightside inner radiation belt enabled by the STEREO Time Domain Sampler. Amplitudes range from 30.110 mV/m (zero ]peak), 2 to 3 orders of magnitude larger than previously observed in this region. Measurements from the peak electric field detector (TDSMax) indicate that these large ]amplitude waves are prevalent throughout the plasmasphere. A detailed examination of high time resolution electric field waveforms is undertaken on a subset of these whistlers at L 100 keV) electrons on a time scale of <1 s and thus may be an important previously unaccounted for source of energization or pitch ]angle scattering in the inner radiation belt.
Ni, B.; Thorne, R. M.; Horne, R. B.; Meredith, N. P.; Shprits, Y.; Chen, L.
2009-12-01
The diffuse aurora constitutes one of the most important loss processes of plasma sheet electrons, supplying the majority of ionizing energy input into the high-latitude region during conditions of both low and high solar wind driving. It is generally agreed that wave-particle interactions, including scattering losses by electrostatic electron cyclotron harmonic (ECH) waves and electromagnetic whistler-mode chorus waves, play an essential role in the occurrence of the diffuse aurora. However, the precise role of each wave mode has remained a source of controversy for many years. To quantify the scattering effects of these two wave modes, we have improved the methodology for computation of quasi-linear diffusion coefficients and adopted statistical wave models based on the survey of ECH waves and chorus using the entire CRRES database. Our results demonstrate that, whistler-mode chorus is the dominant mechanism for loss of injected plasma sheet electrons from the inner magnetosphere (4 1 keV, suggesting rather minor contributions from ECH waves to the diffuse auroral precipitation. Our results also show that the scattering effects on plasma sheet electrons by the waves are strongly dependent on the level of geomagnetic activity.
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Whistler propagation in ionospheric density ducts: Simulations and DEMETER observations
Woodroffe, J. R.; Streltsov, A. V.; Vartanyan, A.; Milikh, G. M.
2013-11-01
On 16 October 2009, the Detection of Electromagnetic Emissions Transmitted from Earthquake Regions (DEMETER) satellite observed VLF whistler wave activity coincident with an ionospheric heating experiment conducted at HAARP. At the same time, density measurements by DEMETER indicate the presence of multiple field-aligned enhancements. Using an electron MHD model, we show that the distribution of VLF power observed by DEMETER is consistent with the propagation of whistlers from the heating region inside the observed density enhancements. We also discuss other interesting features of this event, including coupling of the lower hybrid and whistler modes, whistler trapping in artificial density ducts, and the interference of whistlers waves from two adjacent ducts.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Energy Technology Data Exchange (ETDEWEB)
Bellan, Paul M. [Applied Physics and Materials Science, Caltech, Pasadena, California 91125 (United States)
2014-10-15
If either finite electron inertia or finite resistivity is included in 2D magnetic reconnection, the two-fluid equations become a pair of second-order differential equations coupling the out-of-plane magnetic field and vector potential to each other to form a fourth-order system. The coupling at an X-point is such that out-of-plane even-parity electric and odd-parity magnetic fields feed off each other to produce instability if the scale length on which the equilibrium magnetic field changes is less than the ion skin depth. The instability growth rate is given by an eigenvalue of the fourth-order system determined by boundary and symmetry conditions. The instability is a purely growing mode, not a wave, and has growth rate of the order of the whistler frequency. The spatial profile of both the out-of-plane electric and magnetic eigenfunctions consists of an inner concave region having extent of the order of the electron skin depth, an intermediate convex region having extent of the order of the equilibrium magnetic field scale length, and a concave outer exponentially decaying region. If finite electron inertia and resistivity are not included, the inner concave region does not exist and the coupled pair of equations reduces to a second-order differential equation having non-physical solutions at an X-point.
Nonlinear Dispersion Relation in Wave Transformation
Institute of Scientific and Technical Information of China (English)
李瑞杰; 严以新; 曹宏生
2003-01-01
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1＜kh＜1.5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
Statistical distribution of nonlinear random wave height
Institute of Scientific and Technical Information of China (English)
HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi
2006-01-01
A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.
Investigation of Ionospheric Turbulence and Whistler Wave Interactions with Space Plasmas
2012-11-21
GeoMagnetic Observatory System ( GMO ). We then have detection of HF heater-induced large plasma sheets, using MUIR radar and GPS satellites [Cohen et al...experiments. It is found that the heat wave fronts, which occurred in US, were plausible sources of free energy generating intense gravity waves and...that the heat wave fronts, which occurred in USA, were the plausible sources of free energy, generating intense gravity waves and triggering large
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
On the polarization of nonlinear gravitational waves
Poplawski, Nikodem J.
2011-01-01
We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Modulation of whistler-mode chorus waves by ULF and the effects on auroral precipitation
Jaynes, A. N.; Usanova, M.; Lessard, M.; Takahashi, K.; Ali, A.; Malaspina, D.; Michell, R.; Spanswick, E.; Donovan, E.; Klitzing, C.; Samara, M.; Spence, H. E.; Wygant, J. R.
2016-12-01
In this study, we present simultaneous observations of structured chorus waves being modulated by ULF waves generated as a result of a substorm injection. The in-situ wave data, measured by Van Allen Probes, were observed simultaneously with ground-based observations of pulsating aurora. Theory and observations have linked equatorial VLF waves with pulsating aurora for decades, invoking the process of pitch-angle scattering of 10's keV electrons in the equatorial magnetosphere. Recent satellite studies have strengthened this argument. In this case study, we propose the scenario being one of substorm-driven ULF pulsations modulating chorus waves, and thus providing the driver for pulsating particle precipitation into the Earth's atmosphere. To investigate the modulation of VLF waves further, we use the WHAMP plasma wave dispersion code to simulate this feature through ULF-modulated density variations. The emerging picture shows that ULF and VLF waves can be intimately related, which has implications for wave-particle interactions throughout the inner magnetosphere.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Nonlinear surface waves over topography
Janssen, T.T.
2006-01-01
As ocean surface waves radiate into shallow coastal areas and onto beaches, their lengths shorten, wave heights increase, and the wave shape transforms from nearsinusoidal to the characteristic saw-tooth shapes at the onset of breaking; in the ensuing breaking process the wave energy is cascaded to
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Nonlinear surface waves in photonic hypercrystals
Ali, Munazza Zulfiqar
2017-08-01
Photonic crystals and hyperbolic metamaterials are merged to give the concept of photonic hypercrystals. It combines the properties of its two constituents to give rise to novel phenomena. Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation. Both dielectric and metallic photonic hypercrystals are studied and it is found that nonlinearity limits the infinite divergence of wave vectors of the surface waves. These states exist in the frequency region where the linear surface waves do not exist. It is also shown that the nonlinearity can be used to engineer the group velocity of the resulting surface wave.
Nonlinear water waves with soluble surfactant
Lapham, Gary; Dowling, David; Schultz, William
1998-11-01
The hydrodynamic effects of surfactants have fascinated scientists for generations. This presentation describes an experimental investigation into the influence of a soluble surfactant on nonlinear capillary-gravity waves in the frequency range from 12 to 20 Hz. Waves were generated in a plexiglass wave tank (254 cm long, 30.5 cm wide, and 18 cm deep) with a triangular plunger wave maker. The tank was filled with carbon- and particulate-filtered water into which the soluble surfactant Triton-X-100® was added in known amounts. Wave slope was measured nonintrusively with a digital camera running at 225 fps by monitoring the position of light beams which passed up through the bottom of the tank, out through the wavy surface, and onto a white screen. Wave slope data were reduced to determine wave damping and the frequency content of the wave train. Both were influenced by the presence of the surfactant. Interestingly, a subharmonic wave occurring at one-sixth the paddle-driving frequency was found only when surfactant was present and the paddle was driven at amplitudes high enough to produce nonlinear waves in clean water. Although the origins of this subharmonic wave remain unclear, it appears to be a genuine manifestation of the combined effects of the surfactant and nonlinearity.
Longitudinal nonlinear wave propagation through soft tissue.
Valdez, M; Balachandran, B
2013-04-01
In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
de Soria-Santacruz, M.; Shprits, Y. Y.; Drozdov, A.; Menietti, J. D.; Garrett, H. B.; Zhu, H.; Kellerman, A. C.; Horne, R. B.
2017-05-01
The role of plasma waves in shaping the intense Jovian radiation belts is not well understood. In this study we use a realistic wave model based on an extensive survey from the Plasma Wave Investigation on the Galileo spacecraft to calculate the effect of pitch angle and energy diffusion on Jovian energetic electrons due to upper and lower band chorus. Two Earth-based models, the Full Diffusion Code and the Versatile Electron Radiation Belt code, are adapted to the case of the Jovian magnetosphere and used to resolve the interaction between chorus and electrons at L = 10. We also present a study of the sensitivity to the latitudinal wave coverage and initial electron distribution. Our analysis shows that the contribution to the electron dynamics from upper band chorus is almost negligible compared to that from lower band chorus. For 100 keV electrons, we observe that diffusion leads to redistribution of particles toward lower pitch angles with some particle loss, which could indicate that radial diffusion or interchange instabilities are important. For energies above >500 keV, an initial electron distribution based on observations is only weakly affected by chorus waves. Ideally, we would require the initial electron phase space density before transport takes place to assess the importance of wave acceleration, but this is not available. It is clear from this study that the shape of the electron phase space density and the latitudinal extent of the waves are important for both electron acceleration and loss.
Directory of Open Access Journals (Sweden)
E. E. Woodfield
2013-10-01
Full Text Available Jupiter has the most intense radiation belts of all the outer planets. It is not yet known how electrons can be accelerated to energies of 10 MeV or more. It has been suggested that cyclotron-resonant wave-particle interactions by chorus waves could accelerate electrons to a few MeV near the orbit of Io. Here we use the chorus wave intensities observed by the Galileo spacecraft to calculate the changes in electron flux as a result of pitch angle and energy diffusion. We show that, when the bandwidth of the waves and its variation with L are taken into account, pitch angle and energy diffusion due to chorus waves is a factor of 8 larger at L-shells greater than 10 than previously shown. We have used the latitudinal wave intensity profile from Galileo data to model the time evolution of the electron flux using the British Antarctic Survey Radiation Belt (BAS model. This profile confines intense chorus waves near the magnetic equator with a peak intensity at ∼5° latitude. Electron fluxes in the BAS model increase by an order of magnitude for energies around 3 MeV. Extending our results to L = 14 shows that cyclotron-resonant interactions with chorus waves are equally important for electron acceleration beyond L = 10. These results suggest that there is significant electron acceleration by cyclotron-resonant interactions at Jupiter contributing to the creation of Jupiter's radiation belts and also increasing the range of L-shells over which this mechanism should be considered.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Nonlinear ship waves and computational fluid dynamics
National Research Council Canada - National Science Library
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
.... Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design...
Solar Wind Compression Generation of Coincident EMIC and Whistler Mode Chorus and Hiss Waves
Halford, Alexa; Mann, Ian
2016-07-01
Electron radiation belt dynamics are controlled by the competition of multiple acceleration and loss mechanisms. Electromagnetic ion cyclotron (EMIC), chorus, and hiss waves have all been implicated as potential loss mechanisms of radiation belt electrons along with Chorus waves proposed as a mechanism for accelerating the lower energy source population to MeV energies. Understanding the relative importance of these waves as well as where and under what conditions they are generated is vital to predicting radiation belt dynamics. Although the size of the solar wind compression on 9 January 2014 event discussed here was modest, it has given us an opportunity to observe clearly how a magnetospheric compression can lead to the generation of EMIC, chorus, and hiss waves. The ICME generated shock encountered the Earth's magnetosphere on 9 January 2014 at ~20:11 UT, and the Van Allen Probes observe the coincident excitation of EMIC and Chorus waves outside the plasmasphere, and hiss weaves inside the plasmasphere. As the shock encountered the magnetosphere, an electric field impulse was observed to generate an increase in temperature anisotropy for both ions and electrons. This increased temperature anisotropy led to increased wave growth on both the ion and electron cyclotron branches. The simultaneous generation of multiple types of waves may lead to significant impacts on the acceleration and loss of radiation belt electrons, especially during geomagnetic compressions observed during the substorms, and the storm sudden commencement and main phases of geomagnetic storms, as well as during quiet time sudden impulse events. For example, the excitation of both EMIC and chorus waves at the same place, and at the same time, may complicate studies seeking a causal connection between specific individual plasma wave bursts and observations of particle precipitation into the atmosphere. During this relatively small event BARREL had three payloads in conjunction with the Van
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...
The Nonlinear Talbot Effect of Rogue Waves
Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-01-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a \\pi-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Whistler-Langmuir oscillitons and their relation to auroral hiss
Directory of Open Access Journals (Sweden)
K. Sauer
2011-10-01
Full Text Available A new type of oscilliton (soliton with superimposed spatial oscillations is described which arises in plasmas if the electron cyclotron frequency Ω_{e} is larger than the electron plasma frequency ω_{e}, which is a typical situation for auroral regions in planetary magnetospheres. Both high-frequency modes of concern, the Langmuir and the whistler wave, are completely decoupled if they propagate parallel to the magnetic field. However, for oblique propagation two mixed modes are created with longitudinal and transverse electric field components. The lower mode (in the literature commonly called the whistler mode, e.g. Gurnett et al., 1983 has whistler wave characteristics at small wave numbers and asymptotically transforms into the Langmuir mode. As a consequence of the coupling between these two modes, with different phase velocity dependence, a maximum in phase velocity appears at finite wave number. The occurrence of such a particular point where phase and group velocity coincide creates the condition for the existence of a new type of oscillating nonlinear stationary structure, which we call the whistler-Langmuir (WL oscilliton. After determining, by means of stationary dispersion theory, the parameter regime in which WL oscillitons exist, their spatial profiles are calculated within the framework of cold (non-relativistic fluid theory. Particle-in-cell (PIC simulations are used to demonstrate the formation of WL oscillitons which seem to play an important role in understanding electron beam-excited plasma radiation that is observed as auroral hiss in planetary magnetospheres far away from the source region.
Tao, Xin; Zonca, Fulvio; Chen, Liu
2017-09-01
The evolution of the electron phase space structures during excitation of a triggered emission is investigated using the nonlinear δ f method. Previous studies suggested that the dynamics of phase space structures due to nonlinear wave particle interactions is critical to the excitation of triggered emissions with frequency chirping. We introduce the use of the nonlinear δ f method to simulate triggered emissions. Compared with full-f particle-in-cell method, the nonlinear δ f method significantly reduces numerical noise, therefore making the phase space structures more identifiable. Specific to the simulation of triggered emissions, the nonlinear δ f method also does not show numerical distortion of the distribution function due to reflecting particle boundary conditions. Using the nonlinear δ f method, we show that during the main portion of the chirping element, the phase space structure roughly maintains a shape so that the resonant island moves a distance in phase space that is on the same order as its width during one phase space bounce period of deeply trapped particles, supporting that the interaction is non-adiabatic. We also demonstrate the disappearance of the phase space structure near the end of the chirping. Our work suggests that the nonlinear δ f method could be very useful for the study of excitation of triggered emissions and to understand the mechanism of frequency chirping.
Hartley, D. P.; Kletzing, C. A.; Kurth, W. S.; Bounds, S. R.; Averkamp, T. F.; Hospodarsky, G. B.; Wygant, J. R.; Bonnell, J. W.; Santolík, O.; Watt, C. E. J.
2016-05-01
Cold plasma theory and parallel wave propagation are often assumed when approximating the whistler mode magnetic field wave power from electric field observations. The current study is the first to include the wave normal angle from the Electric and Magnetic Field Instrument Suite and Integrated Science package on board the Van Allen Probes in the conversion factor, thus allowing for the accuracy of these assumptions to be quantified. Results indicate that removing the assumption of parallel propagation does not significantly affect calculated plasmaspheric hiss wave powers. Hence, the assumption of parallel propagation is valid. For chorus waves, inclusion of the wave normal angle in the conversion factor leads to significant alterations in the distribution of wave power ratios (observed/ calculated); the percentage of overestimates decreases, the percentage of underestimates increases, and the spread of values is significantly reduced. Calculated plasmaspheric hiss wave powers are, on average, a good estimate of those observed, whereas calculated chorus wave powers are persistently and systematically underestimated. Investigation of wave power ratios (observed/calculated), as a function of frequency and plasma density, reveals a structure consistent with signal attenuation via the formation of a plasma sheath around the Electric Field and Waves spherical double probes instrument. A simple, density-dependent model is developed in order to quantify this effect of variable impedance between the electric field antenna and the plasma interface. This sheath impedance model is then demonstrated to be successful in significantly improving agreement between calculated and observed power spectra and wave powers.
Nonlinear Landau damping and Alfven wave dissipation
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Tsurutani, Bruce T.; Smith, Edward J.; Brinca, Armando L.; Thorne, Richard M.; Matsumoto, Hiroshi
1989-01-01
The physical characteristics of high-frequency wave packets detected at the steepened edge of magnetosonic waves near Comet Giacobini-Zinner are explored, based on an examination of over 45 well-defined events. The results suggest that the wave packets play an important role in the reorientation and reduction in field magnitude from the steepened magnetosonic waves to the upstream ambient field. The observed properties of the wave packets are shown to be consistent with anomalously Doppler-shifted right-hand polarized waves.
Threlfall, J W; De Moortel, I; McClements, K G; Arber, T D
2012-01-01
Context. This paper investigates the role of the Hall term in the propagation and dissipation of waves which interact with 2D magnetic X-points and considers the effect of the Hall term on the nature of the resulting reconnection. Aims. The goal is to determine how the evolution of a nonlinear fast magnetoacoustic wave pulse, and the behaviour of the oscillatory reconnection which results from the interaction of the pulse with a line-tied 2D magnetic X-point, is affected by the Hall term in the generalised Ohm's law. Methods. A Lagrangian remap shock-capturing code (Lare2d) is used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth (di) in resistive Hall MHD. A magnetic null-point finding algorithm is also used to locate and track the evolution of the multiple null-points that are formed in the system. Results. In general, the fast wave is coupled to a shear wave and, for finite di, to whistler and ion cyclotron waves. Dispersive whistler effects...
Vinas, Adolfo F.; Moya, Pablo S.; Navarro, Roberto; Araneda, Jamie A.
2014-01-01
Two fundamental challenging problems of laboratory and astrophysical plasmas are the understanding of the relaxation of a collisionless plasmas with nearly isotropic velocity distribution functions and the resultant state of nearly equipartition energy density with electromagnetic plasma turbulence. Here, we present the results of a study which shows the role that higher-order-modes play in limiting the electromagnetic whistler-like fluctuations in a thermal and non-thermal plasma. Our main results show that for a thermal plasma the magnetic fluctuations are confined by regions that are bounded by the least-damped higher order modes. We further show that the zone where the whistler-cyclotron normal modes merges the electromagnetic fluctuations shifts to longer wavelengths as the beta(sub e) increases. This merging zone has been interpreted as the beginning of the region where the whistler-cyclotron waves losses their identity and become heavily damped while merging with the fluctuations. Our results further indicate that in the case of nonthermal plasmas, the higher-order modes do not confine the fluctuations due to the effective higher-temperature effects and the excess of suprathermal plasma particles. The analysis presented here considers the second-order theory of fluctuations and the dispersion relation of weakly transverse fluctuations, with wave vectors parallel to the uniform background magnetic field, in a finite temperature isotropic bi-Maxwellian and Tsallis-kappa-like magnetized electron-proton plasma. Our results indicate that the spontaneously emitted electromagnetic fluctuations are in fact enhanced over these quasi modes suggesting that such modes play an important role in the emission and absorption of electromagnetic fluctuations in thermal or quasi-thermal plasmas.
Wilson, L B; Kellogg, P J; Wygant, J R; Goetz, K; Breneman, A; Kersten, K
2011-01-01
We present a statistical study of the characteristics of very large amplitude whistler waves inside the terrestrial magnetosphere using waveform capture data from the Wind spacecraft as an addition of the study by Kellogg et al., [2010b]. We observed 244(65) whistler waves using electric(magnetic) field data from the Wind spacecraft finding ~40%(~62%) of the waves have peak-to-peak amplitudes of >/- 50 mV/m(>/- 0.5 nT). We present an example waveform capture of the largest magnetic field amplitude (>/- 8 nT peak-to-peak) whistler wave ever reported in the radiation belts. The estimated Poynting flux magnitude associated with this wave is >/- 300 microW/m^2, roughly four orders of magnitude above previous estimates. Such large Poynting flux values are consistent with rapid energization of electrons. The majority of the largest amplitude whistlers occur during magnetically active periods (AE > 200 nT). The waves were observed to exhibit a broad range of propagation angles with respect to the magnetic field, 0{\\...
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
Nonlinear Interaction of Waves in Geomaterials
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Distribution of whistler mode bursts at Venus
Scarf, F. L.; Jordan, K. F.; Russell, C. T.
1987-01-01
Several thousand impulsive whistler mode noise bursts were detected by the Pioneer Venus wave instrument during the first 10 seasons with nightside traversals at low altitudes. The altitude distribution for these events shows that essentially all of the bursts were detected when the orbiter was less than 2000 km above the planet, suggesting that the varying plasma conditions could not maintain coherent whistler mode field-aligned guidance over greater distances. Within the 2000-km range, the distribution of the number of events versus altitude shows that there are two distinct subregions. These results are interpreted in terms of two types of whistler mode propagation from sources below the ionosphere.
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Optics in a nonlinear gravitational wave
Harte, Abraham I
2015-01-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. The commonly-used predictions of linear perturbation theory are shown to be generically overshadowed---even for very weak gravitational waves---by nonlinear effects when considering observations of sufficiently distant sources; higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Optics in a nonlinear gravitational plane wave
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Connections between whistlers and pulsation activity
Directory of Open Access Journals (Sweden)
J. Verö
Full Text Available Simultaneous whistler records of one station and geomagnetic pulsation (Pc3 records at three stations were compared. In a previous study correlation was found between occurrence and L value of propagation/excitation for the two phenomena. The recently investigated simultaneous records have shown that the correlation is better on longer time scales (days than on shorter ones (minutes, but the L values of the propagation of whistlers/excitation of pulsations are correlated, i.e. if whistlers propagate in higher latitude ducts, pulsations have periods longer than in the case when whistlers propagate in lower latitude ducts.
Key words: Electromagnetics (wave propagation - Magnetospheric physics (magnetospheric configuration and dynamics; MHD waves and instabilities
Sondhiya, Deepak Kumar; Gwal, Ashok Kumar; Kasde, Satish Kumar
2016-07-01
Symmetric sidebands are observed in the ionosphere by the DEMETER (Detection of Electromagnetic Radiation Transmitted through Earthquake Region) satellite, when it passes above the Indian VLF transmitter, named VTX (18.2 kHz), located near Kanyakumari, India. The spectral boarding phenomena may be divided into two types: (1) spectrally broadened components occurring without any association with ELF/VLF emissions under disturbed ionospheric condition, (2) Spectrally broadened components with predominant side band structure in association with ELF emission. Generally spectral analysis at second order (Power spectrum) is used to analyze the frequency component of signal, but it losses the phase information among the different Fourier components. To retain this information the bispectrum (third order) and/or the bicoherence (normalized bispectrum) are used. Results suggest a non-linear mode coupling between the transmitter signal and ELF emission which produces sidebands that are quasi-electrostatic in nature. However, faint spectral broadened components in both types 1 and 2 may be connected with Doppler shift of quasi-electrostatic, whistler mode waves with a broad spectrum near resonance cone, due to scattering of the transmitter signals from ionospheric irregularities in the F-region. Keywords: spectral boarding, wave-wave Interaction, whistler mode waves and Doppler shift
Generation mechanism of whistler-mode chorus emissions
Omura, Yoshiharu
We describe the nonlinear dynamics of resonant electrons interacting with a coherent whistler-mode wave and the formation of electromagnetic electron holes or hills in the velocity phase space. In the presence of the inhomogeneity due to the frequency variation and the gradient of the magnetic field, the electron holes or hills result in resonant currents generating rising-tone emissions (1, 2) or falling-tone emissions (3), respectively. After formation of a coherent wave at the maximum linear growth rate, triggering of the nonlinear wave growth takes place when the wave amplitude is close to the optimum wave amplitude (4). The wave amplitude also has to be above the threshold amplitude (2) so that the nonlinear wave growth can occur as an absolute instability at the magnetic equator. The triggering process is repeated at progressively higher frequencies in the case of a rising-tone emission, generating subpackets of a chorus element. We also describe the mechanism of nonlinear wave damping due to quasi-oblique propagation from the equator (2), which results in the formation of a gap at half the electron cyclotron frequency, separating a long rising-tone chorus emission into the upper-band and lower-band chorus emissions (5). *References (1) Y. Omura,Y. Katoh, and D. Summers, Theory and simulation of the generation of whistler-mode chorus, J. Geophys. Res., 113, A04223, 2008. (2) Y. Omura, , M. Hikishima, Y. Katoh, D. Summers, and S. Yagitani, Nonlinear mechanisms of lower band and upper band VLF chorus emissions in the magnetosphere, J. Geophys. Res., 114, A07217, 2009. (3) Nunn, D., and Y. Omura, A computational and theoretical analysis of falling frequency VLF emissions, J. Geophys. Res., 117, A08228, 2012. (4) Omura, Y., and D. Nunn, Triggering process of whistler mode chorus emissions in the magnetosphere, J. Geophys. Res., 116, A05205, 2011. (5) S. Kurita, Y. Katoh, Y. Omura, V. Angelopoulos, C. M. Cully, O. Le Contel, and H. Misawa, THEMIS observation of
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
Nonlinear Landau damping of Alfven waves.
Hollweg, J. V.
1971-01-01
Demonstration that large-amplitude linearly or elliptically polarized Alfven waves propagating parallel to the average magnetic field can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfven wave. The damping rate can be large even in a cold plasma (beta much less than 1, but not zero), and the mechanism proposed may be the dominant one in many plasmas of astrophysical interest.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
LIU Xiao; XU JiYao; MA RuiPing
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75-85 km, z =90-110 km and z= 115-130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the horizontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90-110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Dynamics of whistler spheromaks in magnetized plasmas.
Eliasson, B; Shukla, P K
2007-11-16
Recent laboratory experiments [Stenzel et al., Phys. Rev. Lett. 96, 095004 (2006)10.1103/PhysRevLett.96.095004] have demonstrated interesting phenomena of propagating nonlinear whistler structures (spheromaks) and stationary field-reversed configurations, whose magnetic fields exceed the ambient magnetic field strength. Our objective here is to present simulation studies for these nonlinear whistler structures based on the three-dimensional nonlinear electron magnetohydrodynamic equations. The robustness and longevity of the propagating whistler spheromaks found in the experiments are confirmed numerically. Varying the toroidal field of the spheromak in the initial conditions, we find that the polarity and the amplitude of the toroidal field determine the propagation direction and speed of the spheromak. Our simulation results are in excellent agreement with those observed in the laboratory experiments.
Nonlinear plasma wave in magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Bulanov, Sergei V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Prokhorov Institute of General Physics, Russian Academy of Sciences, Moscow 119991 (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region 141700 (Russian Federation); Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Hosokai, Tomonao; Zhidkov, Alexei G. [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Japan Science and Technology Agency, CREST, 2-1, Yamadaoka, Suita, Osaka 565-0871 (Japan); Kodama, Ryosuke [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871 (Japan)
2013-08-15
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic “Four-Ray Star” pattern.
Study of Linear and Nonlinear Wave Excitation
Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick
2013-10-01
We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.
Wave-kinetic description of nonlinear photons
Marklund, M; Brodin, G; Stenflo, L
2004-01-01
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner-Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to break-up and focusing of ultra-high intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser-plasma systems.
A nonlinear Schroedinger wave equation with linear quantum behavior
Energy Technology Data Exchange (ETDEWEB)
Richardson, Chris D.; Schlagheck, Peter; Martin, John; Vandewalle, Nicolas; Bastin, Thierry [Departement de Physique, University of Liege, 4000 Liege (Belgium)
2014-07-01
We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schroedinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear Dispersion Effect on Wave Transformation
Institute of Scientific and Technical Information of China (English)
LI Ruijie; Dong-Young LEE
2000-01-01
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986), and which has a better approximation to Hedges＇ empirical relation than the modilied relations by Hedges (1987). Kirby and Dahymple (1987) for shallow waters. The new dispersion relation is simple in form. thus it can be used easily in practice. Meanwhile. a general explicil approximalion to the new dispersion rela tion and olher nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking inlo account weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed vith the new dispersion relation predicts wave translornation over complicated topography quite well.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Electron beam generated whistler emissions in a laboratory plasma
Energy Technology Data Exchange (ETDEWEB)
Van Compernolle, B., E-mail: bvcomper@physics.ucla.edu; Pribyl, P.; Gekelman, W. [Department of Physics, University of California, Los Angeles (United States); An, X.; Bortnik, J.; Thorne, R. M. [Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles (United States)
2015-12-10
Naturally occurring whistler mode emissions in the magnetosphere, are important since they are responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Recently, we reported on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced [1]. A beam of energetic electrons is launched into a cold plasma and excites both chirping whistler waves and broadband waves. Here we extend our previous analysis by comparing the properties of the broadband waves with linear theory.
Electron beam generated whistler emissions in a laboratory plasma
Van Compernolle, B.; An, X.; Bortnik, J.; Thorne, R. M.; Pribyl, P.; Gekelman, W.
2015-12-01
Naturally occurring whistler mode emissions in the magnetosphere, are important since they are responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Recently, we reported on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced [1]. A beam of energetic electrons is launched into a cold plasma and excites both chirping whistler waves and broadband waves. Here we extend our previous analysis by comparing the properties of the broadband waves with linear theory.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Inertial-range spectrum of whistler turbulence
Directory of Open Access Journals (Sweden)
Y. Narita
2010-02-01
Full Text Available We develop a theoretical model of an inertial-range energy spectrum for homogeneous whistler turbulence. The theory is a generalization of the Iroshnikov-Kraichnan concept of the inertial-range magnetohydrodynamic turbulence. In the model the dispersion relation is used to derive scaling laws for whistler waves at highly oblique propagation with respect to the mean magnetic field. The model predicts an energy spectrum for such whistler waves with a spectral index −2.5 in the perpendicular component of the wave vector and thus provides an interpretation about recent discoveries of the second inertial-range of magnetic energy spectra at high frequencies in the solar wind.
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-06-15
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Characterizing Electron Trapping Nonlinearity in Langmuir Waves
Strozzi, D J; Rose, H A; Hinkel, D E; Langdon, A B; Banks, J W
2012-01-01
We assess when electron trapping nonlinearities are expected to be important in Langmuir waves. The basic criterion is that the effective lifetime, t_d, of resonant electrons in the trapping region of velocity space must exceed the period of trapped motion for deeply-trapped electrons, tau_B = (n_e/delta n)^{1/2} 2pi/omega_pe. A unitless figure of merit, the "bounce number" N_B = t_d/tau_B, encapsulates this condition and allows an effective threshold amplitude for which N_B=1 to be defined. The lifetime is found for convective loss (transverse and longitudinal) out of a spatially finite Langmuir wave. Simulations of driven waves with a finite transverse profile, using the 2D-2V Vlasov code Loki, show trapping nonlinearity increases continuously with N_B for side loss, and is significant for N_B ~ 1. The lifetime due to Coulomb collisions (both electron-electron and electron-ion) is also found, with pitch-angle scattering and parallel drag and diffusion treated in a unified way. A simple way to combine convec...
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity ($\\delta I/I\\sim \\delta n/n$). The waves are evident as significant density fluctuations that vary with height, and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Characteristic properties of Nu whistlers as inferred from observations and numerical modelling
Directory of Open Access Journals (Sweden)
D. R. Shklyar
2004-11-01
Full Text Available The properties of Nu whistlers are discussed in the light of observations by the MAGION 5 satellite, and of numerically simulated spectrograms of lightning-induced VLF emissions. The method of simulation is described in full. With the information from this numerical modelling, we distinguish the characteristics of the spectrograms that depend on the site of the lightning strokes from those that are determined mainly by the position of the satellite. Also, we identify the region in the magnetosphere where Nu whistlers are observed most often, and the geomagnetic conditions favouring their appearance. The relation between magnetospherically reflected (MR whistlers and Nu whistlers is demonstrated by the gradual transformation of MR whistlers into Nu whistlers as the satellite moves from the high-altitude equatorial region to lower altitudes and higher latitudes. The magnetospheric reflection of nonducted whistler-mode waves, which is of decisive importance in the formation of Nu whistlers, is discussed in detail.
Nonlinear Plasma Wave in Magnetized Plasmas
Bulanov, Sergei V; Kando, Masaki; Koga, James K; Hosokai, Tomonao; Zhidkov, Alexei G; Kodama, Ryosuke
2013-01-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern which has been observed in the image of the electron bunch in experiments [T. Hosokai, et al., Phys. Rev. Lett. 97, 075004 (2006)].
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Saturation process of nonlinear standing waves
Institute of Scientific and Technical Information of China (English)
马大猷; 刘克
1996-01-01
The sound pressure of the nonlinear standing waves is distorted as expected, but also tends to saturate as being found in standing-wave tube experiments with increasing sinusoidal excitation. Saturation conditions were not actually reached, owing to limited excitation power, but the evidence of tendency to saturation is without question. It is the purpose of this investigation to find the law of saturation from the existing experimental data. The results of curve fitting indicate that negative feedback limits the growth of sound pressure with increasing excitation, the growth of the fundamental and the second harmonic by the negative feedback of their sound pressures, and the growth of the third and higher harmonics, however, by their energies (sound pressures squared). The growth functions of all the harmonics are derived, which are confirmed by the experiments. The saturation pressures and their properties are found.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...
Nonlinear wave propagation in constrained solids subjected to thermal loads
Nucera, Claudio; Lanza di Scalea, Francesco
2014-01-01
The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such "residual" energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Electron Trapping and Charge Transport by Large Amplitude Whistlers
Kellogg, P. J.; Cattell, C. A.; Goetz, K.; Monson, S. J.; Wilson, L. B., III
2010-01-01
Trapping of electrons by magnetospheric whistlers is investigated using data from the Waves experiment on Wind and the S/WAVES experiment on STEREO. Waveforms often show a characteristic distortion which is shown to be due to electrons trapped in the potential of the electrostatic part of oblique whistlers. The density of trapped electrons is significant, comparable to that of the unperturbed whistler. Transport of these trapped electrons to new regions can generate potentials of several kilovolts, Trapping and the associated potentials may play an important role in the acceleration of Earth's radiation belt electrons.
The nonlinear standing wave inside the space of liquid
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.
Axisymmetric nonlinear waves and structures in Hall plasmas
Energy Technology Data Exchange (ETDEWEB)
Islam, Tanim [Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94551-0808 (United States)
2012-06-15
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.
Axisymmetric Nonlinear Waves And Structures in Hall Plasmas
Islam, Tanim
2011-01-01
A Hall plasma consists of a plasma with not all species frozen into the magnetic field. In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature -- whistler drift modes that propagate along the electron drift as a Burger's shock, and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral -- are analyzed. We derive analytical and numerical solutions in an electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to electron-ion-gas Hall plasmas, in which the ions are coupled to the motion of gases in low ionized plasmas (lower ionosphere and protostellar disks), and to dusty Hall plasmas (such as molecular clouds), in which the much heavier charged dust may be collisionally coupled to the gas.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Sivokon', V. P.; Bogdanov, V. V.; Druzhin, G. I.; Cherneva, N. V.; Kubyshkin, A. V.; Sannikov, D. V.; Agranat, I. V.
2014-11-01
Analysis of the experimental data obtained at Paratunka observatory (53.02° N, 158.65° E; L = 2.3) has revealed a nonstandard form of whistlers involving spectral lines that are symmetric with respect to the whistler. We have shown that this form is most likely due to the amplitude modulation of whistlers by electromagnetic pulses with a length of around 1 s and carrier frequency of around 1.1 kHz. We have suggested that these pulses could be emitted by the auroral electrojet modified by heating radiation from the HAARP facility (62.30° N, 145.30° W; L > 4.2).
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two...
The whistler mode in a Vlasov plasma
Tokar, R. L.; Gary, S. P.
1985-01-01
In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation. To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions. For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate. The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory.
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...... of a constantly maintained pump wave is derived and a general dispersion relation describing the modulation of the high frequency wave due to different low frequency responses is obtained. Particular attention is devoted to a purely growing modulation. The relative importance of the ponderomotive force...
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Distribution of the nonlinear random ocean wave period
Institute of Scientific and Technical Information of China (English)
HOU Yijun; LI Mingjie; SONG Guiting; SI Guangcheng; QI Peng; HU Po
2009-01-01
Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (υ=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Nonlinear numerical simulation on extreme-wave kinematics
Institute of Scientific and Technical Information of China (English)
NING Dezhi; TENG Bin; LIU Shuxue
2009-01-01
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is "adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media (where distortion can be cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
First use of high-res MMS electron distributions to study magnetopause waves
Goldman, Martin; Ergun, R. E.; Lapenta, Giovanni.; Newman, David; Wilder, Frederick
2016-07-01
Fast Plasma Instruments on the MMS satellites have measured 3-D electron distributions at a resolution of 30ms, which is 100 times faster than Cluster and Themis spectrometers. We have carried out a linear theory of parallel-propagating waves based on the measured electron distribution during a period of observed whistler and Langmuir wave activity. Using MMS reduced electron distributions, marginal stability and/or weak growth is found at frequencies near the frequencies of whistlers and Langmuir waves observed at this time by MMS. The parallel phase velocities of whistlers at these frequencies are theoretically found to be very near ±veA/2, where veA = (fec/fep)c is the electron Alfven speed and fec/fep whistler phase velocities parallel to B. This feature may be related to emission from electron or nonlinear bipolar field currents.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Dispersion properties of ducted whistlers, generated by lightning discharge
Directory of Open Access Journals (Sweden)
D. L. Pasmanik
2005-06-01
Full Text Available Whistler-mode wave propagation in magnetospheric ducts of enhanced cold plasma density is studied. The case of the arbitrary ratio of the duct radius to the whistler wavelength is considered, where the ray-tracing method is not applicable. The set of duct eigenmodes and their spatial structure are analysed and dependencies of eigenmode propagation properties on the duct characteristics are studied. Special attention is paid to the analysis of the group delay time of one-hop propagation of the whistler wave packet along the duct. We found that, in contrast to the case of a wide duct, the group delay time in a rather narrow duct decreases as the eigenmode number increases. The results obtained are suggested for an explanation of some types of multi-component whistler signals.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Synchronized whistlers recorded at Varanasi
Indian Academy of Sciences (India)
Rajesh Singh; Ashok K Singh; R P Singh
2003-06-01
Some interesting events of synchronized whistlers recorded at low latitude station Varanasi during magnetic storm period of the year 1977 are presented. The dynamic spectrum analysis shows that the component whistlers are Eckersley whistlers having dispersion 10 s1/2 and 30 s1/2. An attempt has been made to explain the dynamic spectra using lightning discharge generated from magnetospheric sources.
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube
Institute of Scientific and Technical Information of China (English)
DUAN Wen-Shan
2004-01-01
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrodinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change,depending on what kind of inhomogeneity the tube has.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Indian Academy of Sciences (India)
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Nonlinear waves in the terrestrial quasi-parallel foreshock
Hnat, B; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-01-01
We study the applicability of the derivative nonlinear Schr\\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a pseudo-potential is elucidated and, in particular, the importance of canonical representation in the correct interpretation of solutions in this formulation is discussed. Numerical solutions of the DNLS equation are then compared directly with the wave forms observed by Cluster spacecraft. Non harmonic slow variations are filtered out by applying the empirical mode decomposition. We find large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency, followed in time by nearly harmonic low amplitude fluctuations. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfv\\'{e}n speed.
The periodic wave solutions for two systems of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
王明亮; 王跃明; 张金良
2003-01-01
The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long-short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Electron - whistler interaction at the Earth`s bow shock: 1. Whistler instability
Energy Technology Data Exchange (ETDEWEB)
Veltri, P.; Zimbardo, G. [Universita della Calabria, Cosenza (Italy)
1993-08-01
The authors model the interaction of whistler waves with the quasi-perpendicular bow shock observed on Nov 7, 1977. Using a Monte Carlo technique they are able to construct the resulting electron distribution function. This distribution function is asymmetric, and includes a loss cone which the data supports. This distribution function asymmetry is able to drive instabilites which couple to generate additional whister energy. A significant amount of the whistler energy is observed to originate from the region where the loss cone is observed.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2010-10-15
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Nonlinear spin-wave excitations at low magnetic bias fields
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Nonlinear electron acoustic waves in presence of shear magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Statistical distribution of nonlinear random wave height in shallow water
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution.The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated.The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution.The effect of wave steepness in shallow water is similar to that in deep water;but the factor of shallow water lowers the wave height distribution of the general wave with the reduced factor of wave steepness.It also makes the wave height distribution of shallow water more centralized.The results indicate that the new distribution fits the in situ measurements much better than other distributions.
Development of A Fully Nonlinear Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
陈永平; 李志伟; 张长宽
2004-01-01
A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method,the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Nonlinear volume holography for wave-front engineering.
Hong, Xu-Hao; Yang, Bo; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2014-10-17
The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Exact Nonlinear Internal Equatorial Waves in the f-plane
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Experimental observations of nonlinear effects of the Lamb waves
Institute of Scientific and Technical Information of China (English)
DENG Mingxi; D.C. Price; D.A.Scott
2004-01-01
The experimental observations of nonlinear effects of the primary Lamb waves have been reported. Firstly, the brief descriptions have been made for the nonlinear acoustic measurement system developed by Ritec. The detailed considerations for the acoustic experiment system established for observing of the nonlinear effects of the primary Lamb waves have been carried out. Especially, the analysis focuses on the time-domain responses of second harmonics of the primary Lame waves by employing a straightforward model. Based on the existence conditions of strong nonlinearity of the primary Lamb waves, the wedge transducers are designed to generate and detect the primary and secondary waves on the surface of an aluminum sheet. For the different distances between the transmitting and receiving wedge transducers,the amplitudes of the primary waves and the second harmonics on the sheet surface have been measured within a specified frequency range. In the immediate vicinity of the driving frequency,where the primary and the double frequency Lamb waves have the same phase velocities, the quantitative relations of second-harmonic amplitudes with the propagation distance have been analyzed. It is experimentally verified that the second harmonics of the primary Lamb waves do have a cumulative growth effect along with the propagation distance.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Whistler oscillitons revisited: the role of charge neutrality?
Directory of Open Access Journals (Sweden)
F. Verheest
2004-01-01
Full Text Available When studying transverse modes propagating parallel to a static magnetic field, an apparent contradiction arises between the weakly nonlinear results obtained from the derivative nonlinear Schrödinger equation, predicting envelope solitons (where the amplitude is stationary in the wave frame, but the phase is not, and recent results for whistler oscillitons, indicating that really stationary structures of large amplitude are possible. Revisiting this problem in the fluid dynamic approach, care has been taken not to introduce charge neutrality from the outset, because this not only neglects electric stresses compared to magnetic stresses, which is reasonable, but could also imply from Poisson's equation a vanishing of the wave electric field. Nevertheless, the fixed points of the remaining equations are the same, whether charge neutrality is assumed from the outset or not, so that the solitary wave solutions at not too large amplitudes will be very similar. This is borne out by numerical simulations of the solutions under the two hypotheses, showing that the lack of correspondence with the DNLS envelope solitons indicates the limitations of the reductive perturbation approach, and is not a consequence of assuming charge neutrality.
Quantification and prediction of rare events in nonlinear waves
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Linear and nonlinear propagation of water wave groups
Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.
1992-01-01
Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.
GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS
Institute of Scientific and Technical Information of China (English)
GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan
2005-01-01
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
2005-03-22
Refraction Since sin 2 Ogm < sin 2 0r, < 1, the separating curve crosses [12] The standard wave coefficients [Stix, 1962] for a cold zero at w, with...o/ slwa ,tehg-est 00 "q *Mk= *peak=*okK 6.37x10 6.37x10 7.08x 10-’ 0 Qgm Q./2 1)..0 ogm fne/2 Q.. 0 ogm 0.2. Figure 4. The function A11(w) (dashed
Wave Propagation In Strongly Nonlinear Two-Mass Chains
Wang, Si Yin; Herbold, Eric B.; Nesterenko, Vitali F.
2010-05-01
We developed experimental set up that allowed the investigation of propagation of oscillating waves generated at the entrance of nonlinear and strongly nonlinear two-mass granular chains composed of steel cylinders and steel spheres. The paper represents the first experimental data related to the propagation of these waves in nonlinear and strongly nonlinear chains. The dynamic compressive forces were detected using gauges imbedded inside particles at depths equal to 4 cells and 8 cells from the entrance gauge detecting the input signal. At these relatively short distances we were able to detect practically perfect transparency at low frequencies and cut off effects at higher frequencies for nonlinear and strongly nonlinear signals. We also observed transformation of oscillatory shocks into monotonous shocks. Numerical calculations of signal transformation by non-dissipative granular chains demonstrated transparency of the system at low frequencies and cut off phenomenon at high frequencies in reasonable agreement with experiments. Systems which are able to transform nonlinear and strongly nonlinear waves at small sizes of the system are important for practical applications such as attenuation of high amplitude pulses.
Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides
Institute of Scientific and Technical Information of China (English)
Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing
2013-01-01
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Sergej Flach; Mikhail Ivanchenko; Nianbei Li
2011-11-01
We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd indications for an asymptotic low-temperature ∼ 4 and intermediate temperature ∼ 2 laws. These ﬁndings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).
Nonlinear mixing of laser generated narrowband Rayleigh surface waves
Bakre, Chaitanya; Rajagopal, Prabhu; Balasubramaniam, Krishnan
2017-02-01
This research presents the nonlinear mixing technique of two co-directionally travelling Rayleigh surface waves generated and detected using laser ultrasonics. The optical generation of Rayleigh waves on the specimen is obtained by shadow mask method. In conventional nonlinear measurements, the inherently small higher harmonics are greatly influenced by the nonlinearities caused by coupling variabilities and surface roughness between the transducer and specimen interface. The proposed technique is completely contactless and it should be possible to eliminate this problem. Moreover, the nonlinear mixing phenomenon yields not only the second harmonics, but also the sum and difference frequency components, which can be used to measure the acoustic nonlinearity of the specimen. In this paper, we will be addressing the experimental configurations for this technique. The proposed technique is validated experimentally on Aluminum 7075 alloy specimen.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Nonlinear wave propagation in a rapidly-spun fiber.
McKinstrie, C J; Kogelnik, H
2006-09-04
Multiple-scale analysis is used to study linear wave propagation in a rapidly-spun fiber and its predictions are shown to be consistent with results obtained by other methods. Subsequently, multiple-scale analysis is used to derive a generalized Schroedinger equation for nonlinear wave propagation in a rapidly-spun fiber. The consequences of this equation for pulse propagation and four-wave mixing are discussed briefly.
Nonlinear propagation of planet-generated tidal waves
Rafikov, Roman
2001-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process sp...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
Cattell, C A; Breneman, A W; Thaller, S A; Wygant, J R; Kletzing, C A; Kurth, W S
2015-09-28
We show the first evidence for locally excited chorus at frequencies below 0.1 fce (electron cyclotron frequency) in the outer radiation belt. A statistical study of chorus during geomagnetic storms observed by the Van Allen Probes found that frequencies are often dramatically lower than expected. The frequency at peak power suddenly stops tracking the equatorial 0.5 fce and f/fce decreases rapidly, often to frequencies well below 0.1 fce (in situ and mapped to equator). These very low frequency waves are observed both when the satellites are close to the equatorial plane and at higher magnetic latitudes. Poynting flux is consistent with generation at the equator. Wave amplitudes can be up to 20 to 40 mV/m and 2 to 4 nT. We conclude that conditions during moderate to large storms can excite unusually low frequency chorus, which is resonant with more energetic electrons than typical chorus, with critical implications for understanding radiation belt evolution.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Low frequency magnetic signals associated with Langmuir waves
Kellogg, Paul J.; Goetz, K.; Lin, N.; Monson, S. J.; Balogh, A.; Forsyth, R. J.; Stone, R. G.
1992-01-01
With the URAP experiment on Ulysses, low frequency signals with a magnetic component in close time correlation with electrostatic Langmuir waves at the plasma frequency are observed. In most, if not all, of these cases, the Langmuir waves are part of a Type III solar burst. This effect is investigated and it is shown that the low frequency waves are in the whistler mode and are most likely due to nonlinear effects involving Langmuir waves.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
Energy Technology Data Exchange (ETDEWEB)
Xie, Xi-Yang; Tian, Bo, E-mail: tian_bupt@163.com; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Energy Technology Data Exchange (ETDEWEB)
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Simulation of Fully Nonlinear 3-D Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
张晓兔; 滕斌; 宁德志
2004-01-01
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Nonlinear diffraction of water waves by offshore stuctures
Directory of Open Access Journals (Sweden)
Matiur Rahman
1986-01-01
Full Text Available This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
Evaluating the effects of lightning-generated whistlers observed by the DEMETER spacecraft
Zahlava, Jan; Nemec, Frantisek; Pincon, Jean-Louis; Santolik, Ondrej; Kolmasova, Ivana; Parrot, Michel
2016-04-01
Although lightning-generated whistlers have been studied for nearly a century, there are still questions to be answered. It is clear that, at least in a certain frequency range, these waves significantly contribute to the overall wave intensity in the inner magnetosphere. They also influence distribution functions of energetic particles in the van Allen radiation belts. Due to the on board implemented neural network for automated whistler detection, the data set obtained by the low-altitude DEMETER spacecraft allows us to relate measured electromagnetic wave data and energetic particle flux with the number and dispersion of whistlers detected during a certain time interval. We distinguish the cases with high and low whistler occurrence and we use this information to determine the overall effect of lightning-generated whistlers.
Singh, Nagendra
2011-12-01
Despite the widely discussed role of whistler waves in mediating magnetic reconnection (MR), the direct connection between such waves and the MR has not been demonstrated by comparing the characteristic temporal and spatial features of the waves and the MR process. Using the whistler wave dispersion relation, we theoretically predict the experimentally measured rise time (τ(rise)) of a few microseconds for the fast rising MR rate in the Versatile Toroidal Facility at MIT. The rise time is closely given by the inverse of the frequency bandwidth of the whistler waves generated in the evolving current sheet. The wave frequencies lie much above the ion cyclotron frequency, but they are limited to less than 0.1% of the electron cyclotron frequency in the argon plasma. The maximum normalized MR rate R=0.35 measured experimentally is precisely predicted by the angular dispersion of the whistler waves.
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Directory of Open Access Journals (Sweden)
R. Shi
2012-09-01
Full Text Available Compared to the recently improved understanding of nightside diffuse aurora, the mechanism(s responsible for dayside diffuse aurora remains poorly understood. While dayside chorus has been thought as a potential major contributor to dayside diffuse auroral precipitation, quantitative analyses of the role of chorus wave scattering have not been carefully performed. In this study we investigate a dayside diffuse auroral intensification event observed by the Chinese Arctic Yellow River Station (YRS all-sky imagers (ASI on 7 January 2005 and capture a substantial increase in diffuse auroral intensity at the 557.7 nm wavelength that occurred over almost the entire ASI field-of-view near 09:24 UT, i.e., ~12:24 MLT. Computation of bounce-averaged resonant scattering rates by dayside chorus emissions using realistic magnetic field models demonstrates that dayside chorus scattering can produce intense precipitation losses of plasma sheet electrons on timescales of hours (even approaching the strong diffusion limit over a broad range of both energy and pitch angle, specifically, from ~1 keV to 50 keV with equatorial pitch angles from the loss cone to up to ~85° depending on electron energy. Subsequent estimate of loss cone filling index indicates that the loss cone can be substantially filled, due to dayside chorus driven pitch angle scattering, at a rate of ≥0.8 for electrons from ~500 eV to 50 keV that exactly covers the precipitating electrons for the excitation of green-line diffuse aurora. Estimate of electron precipitation flux at different energy levels, based on loss cone filling index profile and typical dayside electron distribution observed by THEMIS spacecraft under similar conditions, gives a total precipitation electron energy flux of the order of 0.1 erg cm^{−2} s^{−1} with ~1 keV characteristic energy (especially when using T01s, which can be very likely to cause intense green-line diffuse aurora activity on the
Nonlinear Alfvén wave dynamics in plasmas
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Diffractive optics based four-wave, six-wave, ..., nu-wave nonlinear spectroscopy.
Miller, R J Dwayne; Paarmann, Alexander; Prokhorenko, Valentyn I
2009-09-15
A detailed understanding of chemical processes requires information about both structure and dynamics. By definition, a reaction involves nonstationary states and is a dynamic process. Structure describes the atomic positions at global minima in the nuclear potential energy surface. Dynamics are related to the anharmonicities in this potential that couple different minima and lead to changes in atomic positions (reactions) and correlations. Studies of molecular dynamics can be configured to directly access information on the anharmonic interactions that lead to chemical reactions and are as central to chemistry as structural information. In this regard, nonlinear spectroscopies have distinct advantages over more conventional linear spectroscopies. Because of this potential, nonlinear spectroscopies could eventually attain a comparable level of importance for studying dynamics on the relevant time scales to barrier crossings and reactive processes as NMR has for determining structure. Despite this potential, nonlinear spectroscopy has not attained the same degree of utility as linear spectroscopy largely because nonlinear studies are more technically challenging. For example, unlike the linear spectrometers that exist in almost all chemistry departments, there are no "black box" four-wave mixing spectrometers. This Account describes recent advances in the application of diffractive optics (DOs) to nonlinear spectroscopy, which reduces the complexity level of this technology to be closer to that of linear spectroscopy. The combination of recent advances in femtosecond laser technology and this single optic approach could bring this form of spectroscopy out of the exclusive realm of specialists and into the general user community. However, the real driving force for this research is the pursuit of higher sensitivity limits, which would enable new forms of nonlinear spectroscopy. This Account chronicles the research that has now extended nonlinear spectroscopy to six-wave
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Magnetic antenna excitation of whistler modes. II. Antenna arrays
Energy Technology Data Exchange (ETDEWEB)
Stenzel, R. L.; Urrutia, J. M. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547 (United States)
2014-12-15
The excitation of whistler modes from magnetic loop antennas has been investigated experimentally. The field topology of the excited wave driven by a single loop antenna has been measured for different loop orientations with respect to the uniform background field. The fields from two or more antennas at different locations are then created by superposition of the single-loop data. It is shown that an antenna array can produce nearly plane waves which cannot be achieved with single antennas. By applying a phase shift along the array, oblique wave propagation is obtained. This allows a meaningful comparison with plane wave theory. The Gendrin mode and oblique cyclotron resonance are demonstrated. Wave helicity and polarization in space and time are demonstrated and distinguished from the magnetic helicity of the wave field. The superposition of two oblique plane whistler modes produces in a “whistler waveguide” mode whose polarization and helicity properties are explained. The results show that single point measurements cannot properly establish the wave character of wave packets. The laboratory observations are relevant for excitation and detection of whistler modes in space plasmas.
Magnetic antenna excitation of whistler modes. I. Basic properties
Energy Technology Data Exchange (ETDEWEB)
Urrutia, J. M.; Stenzel, R. L. [Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547 (United States)
2014-12-15
Properties of magnetic loop antennas for exciting electron whistler modes have been investigated in a large laboratory plasma. The parameter regime is that of large plasma frequency compared to the cyclotron frequency and signal frequency below half the cyclotron frequency. The antenna diameter is smaller than the wavelength. Different directions of the loop antenna relative to the background magnetic field have been measured for small amplitude waves. The differences in the topology of the wave magnetic field are shown from measurements of the three field components in three spatial directions. The helicity of the wave magnetic field and of the hodogram of the magnetic vector in space and time are clarified. The superposition of wave fields is used to investigate the properties of two antennas for small amplitude waves. Standing whistler waves are produced by propagating two wave packets in opposite directions. Directional radiation is obtained with two phased loops separated by a quarter wavelength. Rotating antenna fields, produced with phased orthogonal loops at the same location, do not produce directionality. The concept of superposition is extended in a Paper II to generate antenna arrays for whistlers. These produce nearly plane waves, whose propagation angle can be varied by the phase shifting the currents in the array elements. Focusing of whistlers is possible. These results are important for designing antennas on spacecraft or diagnosing and heating of laboratory plasmas.
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Lower hybrid to whistler mode conversion on a density striation
Camporeale, Enrico; Colestock, Patrick
2013-01-01
When a wave packet composed of short wavelength lower hybrid modes traveling in an homogeneous plasma region encounters an inhomogeneity, it can resonantly excite long wavelength whistler waves via a linear mechanism known as mode conversion. An enhancement of lower hybrid/whistler activity has been often observed by sounding rockets and satellites in the presence of density depletions (striations) in the upper ionosphere. We address here the process of linear mode conversion of lower hybrid to whistler waves, mediated by a density striation, using a scalar-field formalism (in the limit of cold plasma linear theory) which we solve numerically. We show that the mode conversion can effectively transfer a large amount of energy from the short to the long wavelength modes. We also study how the efficiency scales by changing the properties (width and amplitude) of the density striation. We present a general criterion for the width of the striation that, if fulfilled, maximizes the conversion efficiency. Such a cri...
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be...
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Nonlinear scattering of radio waves by metal objects
Shteynshleyger, V. B.
1984-07-01
Nonlinear scattering of radio waves by metal structures with resulting harmonic and intermodulation interference is analyzed from both theoretical and empirical standpoints, disregarding nonlinear effects associated with the nonlinear dependence of the electric or magnetic polarization vector on respectively the electric or magnetic field intensity in the wave propagating medium. Nonlinear characteristics of metal-oxide-metal contacts where the thin oxide film separation two metal surfaces has properties approximately those of a dielectric or a high-resistivity semiconductor are discussed. Tunneling was found to be the principal mechanism of charge carrier transfer through such a contact with a sufficiently thin film, the contact having usually a cubic or sometimes an integral sign current-voltage characteristic at 300 K and usually S-form or sometimes a cubic current-voltage characteristic at 77 K.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
The Gouy phase shift in nonlinear interactions of waves
Lastzka, Nico; Schnabel, Roman
2007-06-01
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ(2)interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Whistlers and related ionospheric phenomena
Helliwell, Robert A
2006-01-01
The investigation of whistlers and related phenomena is a key element in studies of very-low-frequency propagation, satellite communication, the outer ionosphere, and solar-terrestrial relationships. This comprehensive text presents a history of the study of the phenomena and includes all the elements necessary for the calculation of the characteristics of whistlers and whistler-mode signals.An introduction and brief history are followed by a summary of the theory of whistlers and a detailed explanation of the calculation of their characteristics. Succeeding chapters offer a complete atlas of
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-06-27
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Nonlinear waves in a fluid-filled thin viscoelastic tube
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the expo-η, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries (KdV)-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves
Directory of Open Access Journals (Sweden)
Hongjuan Yan
2015-01-01
Full Text Available The nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients β and δ are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients β′ and δ′ versus stress and fatigue life. The relative nonlinear coefficients β′ and δ′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient β′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient δ′, however, the experiment data does not accord with the theoretical model.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Shallow water modal evolution due to nonlinear internal waves
Badiey, Mohsen; Wan, Lin; Luo, Jing
2017-09-01
Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Nonlinear reflection of internal gravity wave onto a slope
Raja, Keshav; Sommeria, Joel; Staquet, Chantal; Leclair, Matthieu; Grisouard, Nicolas; Gostiaux, Louis
2016-04-01
The interaction of internal waves on sloping topography is one of the processes that cause mixing and transport in oceans. The mixing caused by internal waves is considered to be an important source of energy that is needed to bring back deep, dense water from the abyss to the surface of the ocean, across constant density surfaces. Apart from the vertical transport of heat (downwards) and mass (upwards), internal waves are also observed to irreversibly induce a mean horizontal flow. Mixing and wave induced mean flow may be considered as the processes that transfer wave induced energy to smaller and larger scales respectively. The process of mixing has been a subject of intense research lately. However, the process of wave induced mean flow and their dynamic impact await thorough study. The present study involves this wave induced mean flow, its generation and energetics. The nonlinear subcritical reflection of internal waves from a sloping boundary is studied using laboratory experiments carried out on the Coriolis Platform at Grenoble and, 2D and 3D numerical simulations done using a non-hydrostatic code. In the experiment, a plane wave is produced using a wave generator and is made to reflect normally on a sloping bottom in a uniformly stratified fluid. We consider both rotating and non-rotating cases. The numerical simulation mimicks the laboratory setup with an initial condition of an analytical plane wave solution in a vertical plane limited by a smooth envelope to simulate the finite wave generator. The interaction of the incident and reflected waves produce, apart from higher harmonics, an irreversible wave induced mean flow which grows in time and is localised in the interacting region. The finite extent of the wave generator allows the mean flow to recirculate in the horizontal plane, resulting in a dipolar potential vorticity field. Moreover, the generation of mean flow and higher harmonics, along with dissipative effects, diminishes the amplitude of
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Electron - whistler interaction at the Earth`s bow shock: 2. Electron pitch angle diffusion
Energy Technology Data Exchange (ETDEWEB)
Veltri, P.; Zimbardo, G. [Universita della Calabria, Cosenza (Italy)
1993-08-01
In this paper the authors further examine the interactions of whistler waves with electrons in the bow shock, simulating a crossing made on Nov 7, 1977. The authors consider the effects of whistler waves and electrostatic noise on the electron distribution function, using a Monte Carlo technique. Their simulations are able to reproduce the moments of the distribution function, including spatial and velocity profiles. They conclude that the fields in the bow shock accelerate electrons, creating asymmetric distributions, which are filled in due to diffusion caused by the electrostatic noise, and which have the velocity distributions balanced due to pitch angle scattering of parallel electrons from whistler waves.
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Analysis of nonlinear internal waves in the New York Bight
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Nonlinear dynamics of Airy-Vortex 3D wave packets: Emission of vortex light waves
Driben, Rodislav
2014-01-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Due to the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and non-zero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse, especially those having small width.
Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.
Driben, Rodislav; Meier, Torsten
2014-10-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.
Linear and Nonlinear Surface Waves in Electrohydrodynamics
Hunt, Matthew; Vanden-broeck, Jean-Marc; Papageorgiou, Demetrios
2015-01-01
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.
Directory of Open Access Journals (Sweden)
F. Lefeuvre
2007-06-01
Full Text Available During a routine analysis of whistlers on the wide-band VLF recording of the DEMETER satellite, a specific signal structure of numerous fractional-hop whistlers, termed the "Spiky Whistler" (SpW was identified. These signals appear to be composed of a conventional whistler combined by the compound mode-patterns of guided wave propagation, suggesting a whistler excited by a lightning "tweek" spheric. Rigorous, full-wave modelling of tweeks, formed by the long subionospheric guided spheric propagation and of the impulse propagation across an arbitrarily inhomogeneous ionosphere, gave an accurate description of the SpW signals. The electromagnetic impulses excited by vertical, preferably CG lightning discharge, exhibited the effects of guided behaviour and of the dispersive ionospheric plasma along their paths. This modelling and interpretation provides a consistent way to determine the generation and propagation characteristics of the recorded SpW signals, as well as to describe the traversed medium.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
A Numerical Wave Tank for Nonlinear Waves with Passive Absorption
Institute of Scientific and Technical Information of China (English)
周宗仁; 尹彰; 石瑞祥
2001-01-01
A numerical wave tank with passive absorption for irregular waves is considered in this paper. Waves with spectralshapes corresponding to that of the Mitsuyasu-Bretschneider type are used as the initial condition at one end of theflume. An absorbing boundary is imposed at the other end of the wave flume to minimize reflection. By use of aLagrangian description for the surface elevation, and finite difference for approximation of the time derivative, the problem is then solved by the boundary element method. The effects of the absorbing boundary are investigated by varyingthe values of the absorption coefficient μ, and studying the time histories of the surface elevations "recorded" on pre-se-lected locations.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Nonlinear wave mechanics from classical dynamics and scale covariance
Energy Technology Data Exchange (ETDEWEB)
Hammad, F. [Departement TC-SETI, Universite A.Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2007-10-29
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Exact controllability for a nonlinear stochastic wave equation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The exact controllability for a semilinear stochastic wave equation with a boundary control is established. The target and initial spaces are L 2 ( G × H −1 ( G with G being a bounded open subset of R 3 and the nonlinear terms having at most a linear growth.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
NUMERICAL SIMULATIONS OF NONLINEAR WAVE TRANSFORMATION AROUND WAVE-PERMEABLE STRUCTURE
Institute of Scientific and Technical Information of China (English)
Li Xi; YAN Yi-xin
2005-01-01
The problem of wave partial/full reflection and transmission by wave-permeable structure is approached by solving the shape-related function with focus on the understanding of wave attenuation.2D depth-averaged Boussinesq type wave equations are given with new damping item in simulating the nonlinear wave transmission through wave-permeable structure.1D wave equation is examined to give the analytical expression of the absorbing coefficient, and is compared with laboratory data in flume to calibrate the coefficients, and the expression is applied directly in modified Boussinesq type equations.Compared with wave basin data for various incident wave conditions,the accurate predictions of combined diffraction-refraction effects in simulating nonlinear wave going through wave-permeable breakwater in the engineering application can be obtained.It shows that wave-permeable breakwaters with proper absorbing effects can be used as an effective alternative to massive gravity breakwaters in reduction of wave transmission in shallow water.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Nonlinear single Compton scattering of an electron wave-packet
Angioi, A; Di Piazza, A
2016-01-01
In the presence of a sufficiently intense electromagnetic laser field, an electron can absorb on average a large number of photons from the laser and emit a high-energy one (nonlinear single Compton scattering). The case of nonlinear single Compton scattering by an electron with definite initial momentum has been thoroughly investigated in the literature. Here, we consider a more general initial state of the electron and use a wave-packet obtained as a superposition of Volkov wave functions. In particular, we investigate the energy spectrum of the emitted radiation at fixed observation direction and show that in typical experimental situations the sharply peaked structure of nonlinear single Compton scattering spectra of an electron with definite initial energy is almost completely washed out. Moreover, we show that at comparable uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency, relate...
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Evolution of Nonlinear Internal Waves in China Seas
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Weak bond detection in composites using highly nonlinear solitary waves
Singhal, Taru; Kim, Eunho; Kim, Tae-Yeon; Yang, Jinkyu
2017-05-01
We experimentally investigate a diagnostic technique for identifying a weak bond in composites using highly nonlinear solitary waves (HNSWs). We set up a one-dimensional chain of granular crystals, consisting of spherical particles with nonlinear interactions, to generate HNSWs. These solitary wave packets are transmitted into an inspection area of composites by making a direct contact with the chain. We demonstrate that a strong type of solitary waves injected to the weak bond area can break the weak bond of laminates, thereby causing delamination. Then, to identify the creation of the delamination, we transmit a weak type of solitary waves by employing the same apparatus, and measure the solitary waves reflected from the specimens. By analyzing these reflected solitary waves, we differentiate the weak bond samples with the pristine bond ones in an efficient and fast manner. The diagnostic results based on the proposed method are compared with the strength and energy release rate at bond interfaces, which are measured via standard testing methods such as three point bending and end notched flexure tests. This study shows the potential of solitary wave-based detection of weak bonds for hot spot monitoring of composite-based structures.
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Nonlinear dynamic behaviors of a floating structure in focused waves
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
On the transition between the Weibel and the whistler instabilities
Palodhi, L; Pegoraro, F; 10.1088/0741-3335/52/9/09500
2010-01-01
The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial modulation of the amplitude of the magnetic field generated by the whistler instability.
Alfven waves in the solar atmosphere. III - Nonlinear waves on open flux tubes
Hollweg, J. V.; Jackson, S.; Galloway, D.
1982-01-01
Consideration is given the nonlinear propagation of Alfven waves on solar magnetic flux tubes, where the tubes are taken to be vertical, axisymmetric and initially untwisted and the Alfven waves are time-dependent axisymmetric twists. The propagation of the waves into the chromosphere and corona is investigated through the numerical solution of a set of nonlinear, time-dependent equations coupling the Alfven waves into motions that are parallel to the initial magnetic field. It is concluded that Alfven waves can steepen into fast shocks in the chromosphere, pass through the transition region to produce high-velocity pulses, and then enter the corona, which they heat. The transition region pulses have amplitudes of about 60 km/sec, and durations of a few tens of seconds. In addition, the Alfven waves exhibit a tendency to drive upward flows, with many of the properties of spicules.
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates
Institute of Scientific and Technical Information of China (English)
CAI Hong-Qiang; YANG Shu-Rong; XUE Ju-Kui
2011-01-01
The dynamics of the weak nonlinear matter solitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BEGs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation freauencv are also obtained.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
Nonlinear waves in electromigration dispersion in a capillary
Christov, Ivan C
2016-01-01
We construct exact solutions to an unusual nonlinear advection--diffusion equation arising in the study of Taylor--Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions ({\\it i.e.}, non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approx...
Liu, Chang
2015-01-01
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the ?first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Landau damping of magnetospherically reflected whistlers
Thorne, Richard M.; Horne, Richard B.
1994-01-01
Unducted VLF signals produced by lightning activity can form a population of magnetospherically reflected (MR) whistlers in the inner magnetosphere. It has been suggested recently that in the absence of significant attenuation such waves could merge into a broadband continuum with sufficient intensity to account for plasmaspheric hiss. To test this conjecture we have evaluated the path-integrated attenuation of MR whistlers along representative ray paths using the HOTRAY code. Using a realistic plasma distribution modeled on in-situ data, we find that the majority of MR waves experience significant damping after a few transits across the equator. This is primarily due to Landau resonance with suprathermal (0.1-1 keV) electrons. The attenuation is most pronounced for waves that propagate through the outer plasmasphere; this can readily account for the infrequent occurrence of multiple-hop MR waves for L greater than or equal to 3.5. Selected waves that originate at intermediate latitudes (15 deg is less than or equal to lambda is less than or equal to 35 deg) and whose ray paths are confined to the inner plasma- sphere may experience up to 10 magnetospheric reflections before substantial attentuation occurs. These waves should form the population of observed MR waves. Wave attenuation becomes more pronounced at higher frequencies; this can account for the absence of multiple-hop waves above 5 kHz. Weakly attenuated MR waves tend to migrate outward to the L shell, where their frequency is comparable to the equatorial lower hybrid frequency. The enhanced concentration of waves due to a merging of ray paths would produce a spectral feature that rises in frequency at lower L. This is quite distinct from the reported properties of plasmaspheric hiss, which maintains a constant frequency band throughout the entire plasmasphere. Furthermore, in the absence of mode conversion, waves below 500 Hz, which often form an important if not dominant part of the spectral properties
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and cur...
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2006-08-15
Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method is applied to three nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Generation and propagation of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.
2007-01-01
During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
Resonant and non-resonant whistlers-particle interaction in the radiation belts
Camporeale, Enrico
2014-01-01
We study the wave-particle interactions between lower band chorus whistlers and an anisotropic tenuous population of relativistic electrons. We present the first direct comparison of first-principle Particle-in-Cell (PIC) simulations with a quasi-linear diffusion code, in this context. In the PIC approach, the waves are self-consistently generated by a temperature anisotropy instability that quickly saturates and relaxes the system towards marginal stability. We show that the quasi-linear diffusion and PIC results have significant quantitative mismatch in regions of energy/pitch angle where the resonance condition is not satisfied. Moreover, for pitch angles close to the loss cone the diffusion code overestimates the scattering, particularly at low energies. This suggest that higher order nonlinear theories should be taken in consideration in order to capture non-resonant interactions, resonance broadening, and to account for scattering at angles close to $90^\\circ$.
Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper studied spherical pulses of solutions of the system of semilinear wave equations with the pulses focusing at a point in three space variables. It is shown that there is no nonlinear effect at leading terms of pulses, when the initial data is subcritical.
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Geodesic deviation in a nonlinear gravitational wave spacetime
Culetu, Hristu
2016-01-01
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\\xi^{v}$ and $\\xi^{u}$ of the separation vector behave as in flat space but the transversal components $\\xi^{x}$ and $\\xi^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
Traveling wave solutions for some factorized nonlinear PDEs
Cornejo-Pérez, Octavio
2009-01-01
In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers-Fisher equation, the Burgers-Fisher equation and a nonlinear dispersive-dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive-dissipative equation are provided.
Detecting nonlinear acoustic waves in liquids with nonlinear dipole optical antennae
Maksymov, Ivan S
2015-01-01
Ultrasound is an important imaging modality for biological systems. High-frequency ultrasound can also (e.g., via acoustical nonlinearities) be used to provide deeply penetrating and high-resolution imaging of vascular structure via catheterisation. The latter is an important diagnostic in vascular health. Typically, ultrasound requires sources and transducers that are greater than, or of order the same size as the wavelength of the acoustic wave. Here we design and theoretically demonstrate that single silver nanorods, acting as optical nonlinear dipole antennae, can be used to detect ultrasound via Brillouin light scattering from linear and nonlinear acoustic waves propagating in bulk water. The nanorods are tuned to operate on high-order plasmon modes in contrast to the usual approach of using fundamental plasmon resonances. The high-order operation also gives rise to enhanced optical third-harmonic generation, which provides an important method for exciting the higher-order Fabry-Perot modes of the dipole...
NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER
Institute of Scientific and Technical Information of China (English)
菅永军; 鄂学全; 柏威
2003-01-01
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
Hilditch, David; Weyhausen, Andreas; Dietrich, Tim; Bruegmann, Bernd; Montero, Pedro J; Mueller, Ewald
2013-01-01
We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -- Brill and Teukolsky waves -- and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -- in particular negative amplitudes -- Brill data can be evolved with moving-puncture coordinates, and behave similarly t...
Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture
Khazanov, G. V.; Krivorutsky, E. N.; Gallagher, D. L.
1999-01-01
The longitudinal and transverse modulation instability of whistler waves in plasma, with a small admixture of hot anisotropic electrons, is discussed. If the hot particles temperature anisotropy is positive, it is found that, in such plasma, longitudinal perturbations can lead to soliton formation for frequencies forbidden in cold plasma. The soliton is enriched by hot particles. The frequency region unstable to transverse modulation in cold plasma in the presence of hot electrons is divided by stable domains. For both cases the role of hot electrons is more significant for whistlers with smaller frequencies.
Observations of unusual whistlers during daytime at Jammu
Indian Academy of Sciences (India)
K K Singh; R P Patel; J Singh; B Kumar; A K Singh; R P Singh; B L Koul; Lalmani
2008-06-01
In this paper,we report observations of unusual whistlers recorded at Jammu (geomag.lat.= 22° 26′N; =1.17), India on March 8, 1999 during the daytime. They are interpreted as one-hop ducted whistlers having propagated along higher -values in closely spaced narrow ducts from the opposite hemispheres. After leakage from the duct, the waves might have propagated in the earthionosphere waveguide towards the equator in surface mode.Tentative explanation of the dynamic spectra of these events is brieﬂy presented.
2-D Composite Model for Numerical Simulations of Nonlinear Waves
Institute of Scientific and Technical Information of China (English)
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
The Nonlinear Landau Damping Rate of a Driven Plasma Wave
Energy Technology Data Exchange (ETDEWEB)
Benisti, D; Strozzi, D J; Gremillet, L; Morice, O
2009-08-04
In this Letter, we discuss the concept of the nonlinear Landau damping rate, {nu}, of a driven electron plasma wave, and provide a very simple, practical, analytic formula for {nu} which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. {nu} actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of {nu} to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Multisymplectic five-point scheme for the nonlinear wave equation
Institute of Scientific and Technical Information of China (English)
WANG Yushun; WANG Bin; YANG Hongwei; WANG Yunfeng
2003-01-01
In this paper, we introduce the multisymplectic structure of the nonlinear wave equation, and prove that the classical five-point scheme for the equation is multisymplectic. Numerical simulations of this multisymplectic scheme on highly oscillatory waves of the nonlinear Klein-Gordon equation and the collisions between kink and anti-kink solitons of the sine-Gordon equation are also provided. The multisymplectic schemes do not need to discrete PDEs in the space first as the symplectic schemes do and preserve not only the geometric structure of the PDEs accurately, but also their first integrals approximately such as the energy, the momentum and so on. Thus the multisymplectic schemes have better numerical stability and long-time numerical behavior than the energy-conserving scheme and the symplectic scheme.
Collapse of nonlinear electron plasma waves in a plasma layer
Grimalsky, V.; Koshevaya, S.; Rapoport, Yu; Kotsarenko, A.
2016-10-01
The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
Electromagnetic Whistler Precursors at Supercritical Interplanetary Shocks
Wilson, L. B., III
2012-01-01
We present observations of electromagnetic precursor waves, identified as whistler mode waves, at supercritical interplanetary shocks using the Wind search coil magnetometer. The precursors propagate obliquely with respect to the local magnetic field, shock normal vector, solar wind velocity, and they are not phase standing structures. All are right-hand polarized with respect to the magnetic field (spacecraft frame), and all but one are right-hand polarized with respect to the shock normal vector in the normal incidence frame. Particle distributions show signatures of specularly reflected gyrating ions, which may be a source of free energy for the observed modes. In one event, we simultaneously observe perpendicular ion heating and parallel electron acceleration, consistent with wave heating/acceleration due to these waves.
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Numerical Simulation of Seabed Response and Liquefaction due to Non-linear Waves
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-feng; ZHANG Qing-he; HAN Tao; QIN Chong-ren
2005-01-01
Based on Biot's consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-linearity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Indian Academy of Sciences (India)
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.
Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi
2008-03-01
In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.
Identification and determination of solitary wave structures in nonlinear wave propagation
Energy Technology Data Exchange (ETDEWEB)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs.
Spectrograms of ship wakes: identifying linear and nonlinear wave signals
Pethiyagoda, Ravindra; Moroney, Timothy J
2016-01-01
A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified three additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. Further, we show that additional features in the experimental data are caused by nonlinearity. Finally, we explain a discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceler...
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Nonlinear Propagation of Planet-Generated Tidal Waves
Rafikov, R. R.
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.
Nonlinear propagation of planet-generated tidal waves
Rafikov, R R
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of the order 1-10 Myr even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed which could be incorporated into the study of gap formation in a gaseous disk around the planet.
New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
Rezzolla, L
2002-01-01
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Probabilistic approach to nonlinear wave-particle resonant interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Analytical description of nonlinear acoustic waves in the solar chromosphere
Litvinenko, Yuri E.; Chae, Jongchul
2017-02-01
Aims: Vertical propagation of acoustic waves of finite amplitude in an isothermal, gravitationally stratified atmosphere is considered. Methods: Methods of nonlinear acoustics are used to derive a dispersive solution, which is valid in a long-wavelength limit, and a non-dispersive solution, which is valid in a short-wavelength limit. The influence of the gravitational field on wave-front breaking and shock formation is described. The generation of a second harmonic at twice the driving wave frequency, previously detected in numerical simulations, is demonstrated analytically. Results: Application of the results to three-minute chromospheric oscillations, driven by velocity perturbations at the base of the solar atmosphere, is discussed. Numerical estimates suggest that the second harmonic signal should be detectable in an upper chromosphere by an instrument such as the Fast Imaging Solar Spectrograph installed at the 1.6-m New Solar Telescope of the Big Bear Observatory.
Nonlinear Electromagnetic Waves in a Degenerate Electron-Positron Plasma
El-Labany, S. K.; El-Taibany, W. F.; El-Samahy, A. E.; Hafez, A. M.; Atteya, A.
2015-08-01
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed.
Irregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2011-01-01
Forces on a monopile from a nonlinear irregular unidirectional wave model are investigated. Two seabed profiles of different slopes are considered. Morison’s equation is used to investigate the forcing from fully nonlinear irregular waves and to compare the results with those obtained from linear...... wave theory and with stream function wave theory. The latter of these theories is only valid on a flat bed. The three predictions of wave forces are compared and the influence of the bed slope is investigated. Force-profiles of two selected waves from the irregular wave train are further compared...... with the corresponding forceprofiles from stream function theory. The results suggest that the nonlinear irregular waves give rise to larger extreme wave forces than those predicted by linear theory and that a steeper bed slope increases the wave forces both for linear and nonlinear waves. It is further found...