Nonlinear Wave Coupling Research Articles

On the origin of microwave zebra pattern

The results of the first observations of a zebra pattern at frequencies around 5.6 GHz are presented. The fine structures in the emission spectrum were recorded simultaneously by the Siberian Solar Radiotelescope and the spectropolarimeters of the National Astronomical Observatories, which allowed us to study the presented event with high spatial, temporal and spectral resolution. The apparent source size does not exceed 10 arcsec, and the sources of the different stripes of the zebra structure coincide spatially. The circular polarization degree reaches 100%, and the polarization sense corresponds to the extraordinary wave. We argue that the most probable generation mechanism of the zebra pattern is nonlinear coupling of Bernstein waves. In this case the value of the magnetic field in the burst source, determined by the frequency separation between the adjacent stripes, is 60-80 G.

Radio signatures of Langmuir-Alfvén turbulence in the solar atmosphere

Radio emissions from the solar active regions can be generated by nonlinear coupling of Langmuir waves with Alfvén waves. Multi-wavelength observations can be used to provide evidence for Langmuir-Alfvén turbulence in the solar atmosphere.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Observation of parametric decay spectrum in a cylindrical electron cyclotron resonance plasma system

Nonlinear wave coupling phenomena in an electron cyclotron resonance (ECR) produced plasma are observed. Experiments are carried out in a small linear cylindrical system with hydrogen plasma. Microwave power in the system is delivered by a magnetron at 2.45 GHz in TE10 mode and is launched radially to have extraordinary (X) wave in plasma. The axial magnetic field configuration, required for ECR to occur in the system, is such that the first ECR surface (B=875 G) resides at the center of the system. Parametric decay spectrum of the launched electromagnetic wave is observed at the upper hybrid resonance (UHR) layer with the appearance of sidebands on the higher and lower side of the launched frequency. Experiments show that the appearance of parametric decay spectrum has a threshold on input microwave power. The decay spectrum is observed only at the UHR surface indicating strong spatial dependence. The parametric decay is also verified in argon and helium plasmas.

The nonlinear coupling of electromagnetic ion cyclotron and lower hybrid waves in the ring current region: the magnetic storm 1-7May 1998

Abstract. The excitation of lower hybrid waves (LHWs) is a widely discussed mechanism of interaction between plasma species in space, and is one of the unresolved questions of magnetospheric multi-ion plasmas. In this paper we present the morphology, dynamics, and level of LHW activity generated by electromagnetic ion cyclotron (EMIC) waves during the 2-7 May 1998 storm period on the global scale. The LHWs were calculated based on a newly developed self-consistent model (Khazanov et. al., 2002) that couples the system of two kinetic equations: one equation describes the ring current (RC) ion dynamic, and another equation describes the evolution of EMIC waves. It is found that the LHWs are excited by helium ions due to their mass dependent drift in the electric field of EMIC waves. The level of LHW activity is calculated assuming that the induced scattering process is the main saturation mechanism for these waves. The calculated LHWs electric fields are consistent with the observational data.

Helical Tomography of an Accretion Disk by Superhump Light Curves of the 2001 Outburst of WZ Sagittae

Abstract A new method for analyzing complex superhump light curves for the 2001 outburst of WZ Sagittae is proposed. The complexity arises because intrinsically time-varying and non-axisymmetric distributions of superhump light sources are coupled with the aspect effects around the binary orbital phase because of its high orbital inclination. The new method can disentangle these complexities by separating the non-axisymmetric spatial distribution in the disk from the time variation with the superhump period. It may be called a helical tomography of an accretion disk because it can reconstruct a series of disk images (i.e., disk’s azimuthal structures) at different superhump phases. The power spectral data of superhump light curves of the 2001 outburst of WZ Sge by Patterson et al. (2002, PASP, 114, 721) are now interpreted under a new light based on the concept of helical tomography, and the azimuthal wave numbers of various frequency modes are identified. In particular, a frequency component, $n\omega_0-\Omega$, where $\omega_0$ and $\Omega$ are the orbital frequency and a low frequency of the apsidal precession of the eccentric disk, is understood as an $(n-1)$-armed traveling wave in the disk. A vigorous excitation of a wave component of $\cos(2\Theta-3\omega_0 t)$ in the first week of the superhump era of WZ Sge, where $\Theta$ is the azimuthal angle, supports Lubow’s (1991, AAA 54.064.175) theory of non-linear wave coupling of the eccentric Lindblad resonance for the superhump phenomenon. This method can in principle be applied to other SU UMa stars with high orbital inclination if light curves are fully covered over the beat cycle.

Nonlinear Damping of Fast Waves and Plasma Heating in the Solar Corona

A nonlinear mechanism for the damping of fast magnetoacoustic wave in the solar corona is studied. It is shown that the nonlinear coupling of finite-amplitude fast waves to small-scale Alfven waves can be much faster than damping mechanisms involving classic transport coefficients.

Internally driven spatiotemporal irregularity in a dc glow discharge

Spatiotemporal dynamics of an undriven dc glow discharge at intermediate pressures (p(0)r(0)=6.2 Torr cm, i<50 mA) is investigated experimentally. Spatiotemporal irregularity and windows of regular nonlinear waves occur and are found to depend on the discharge current. Above a threshold current column head oscillations arise and inject high-frequency ionization waves into the positive column that decay towards the anode through nonlinear wave coupling with a discrete eigenmode of the positive column. Regularity was found to be a result of commensuration of both waves and obeys a devil's staircase. Since column head oscillations occur in the transition region from cathode fall to positive column as result of discharge formation, the irregularities were internally driven. Spatiotemporal analysis by means of biorthogonal decomposition gives insights into the mechanism of irregularity and can be employed for characterization of spatiotemporal complexity.

Generation of circularly polarized radio waves within magnetic holes of the solar wind

The possibility of nonlinear interaction between Langmuir waves and ion–acoustic waves in the solar wind has received considerable interest in the last years. However, little attention has been paid to the possibility of nonlinear coupling between Langmuir waves and whistler waves in the interplanetary medium. Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations within magnetic holes of the solar wind, we develop a nonlinear three-wave theory describing the parametric interaction of Langmuir waves, electromagnetic whistler waves with either right- or left-hand circularly polarized electromagnetic waves. We suggest that the nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind.

Evidence for nonlinear coupling of planetary waves and tides in the lower thermosphere over Bulgaria

Analyses of hourly values of zonal and meridional wind near 95 km observed by meteor radar at Yambol (42.5°N, 26.6°E) during January 1991–June 1992 indicate the presence of planetary waves with prevailing periods of 1.5–2.5, 4–6, 9–10 and 16–18 days. About 20% of the whole power of atmospheric motions is connected with these waves, so they play an important role in the dynamics of the mesosphere-lower thermosphere (MLT) region. By dynamic spectral analysis applied to the hourly neutral wind and to the calculated hourly values of tidal amplitudes it has been demonstrated that there is considerable modulation of tidal amplitudes by planetary waves in the neutral wind, as this process is better expressed in the semidiurnal tides. The nonlinear interaction between tides and planetary waves is studied by bispectral analysis. The results of these analyses indicate again that the nonlinear interactions between semidiurnal tides and planetary waves with periods 2–20 days are stronger than those of the diurnal tides and planetary waves. A peculiar feature of dynamics in the MLT region above Bulgaria is the presence of strong oscillations with periods of 20 and 30 h, which indicate significant nonlinear coupling between them.

Nonlinear Dynamics and Chaos in Space Plasmas

The theory and observation of nonlinear wave coupling phenomena in solar-system plasmas are reviewed. Rocket and satellite observations have provided evidence of nonlinear wave interactions in space plasmas, in particular, in relation to the generation and propagation of radio waves in solar corona, interplanetary medium and Earth’s magnetosphere. These radio waves represent the electromagnetic signature of solar-terrestrial coupling and are useful for forecasting and monitoring of space weather. Nonlinear wave-wave coupling in plasmas can be modeled as a dynamical system of coupled oscillators involving one, two or higher-order wave triplets. For a three-wave dissipative system, the temporal transition from order to chaos may evolve via period doubling or intermittence. For a four-wave Hamiltonian system involving two coupled wave triplets, the spatiotemporal transition from order to chaos is analyzed using the concepts of stable and unstable homogeneous manifolds. Plasma dynamics is governed by a variety of wave motions resulting from the collective electrodynamic interactions involving plasma fields and plasma particles. Nonlinear wave-wave coupling in plasmas can occur due to the growth of parametric instabilities. In this paper, we present an overview of theoryand observation of nonlinear mode coupling in space plasmas. In §2 we discuss the theoryof nonlinear interaction involving a single wave triplet in the presence of source and dissipation. We consider the transition from order to low-dimensional temporal chaos. In § 3w e discuss the theoryof nonlinear interaction involving two wave triplets in the absence of source and dissipation. We treat the transition from order to high-dimensional spatiotemporal chaos. Before discussing the theorylet us first summarize some recent observational evidence of nonlinear wave-wave interactions in the solar system. Comprehensive reviews of this topic are given in Refs. 1) and 2). Radio waves provide the electromagnetic signature of solar-terrestrial relation and serve as a tool to forecast and monitor the space weather. The radio emis

Nonlinear Coupling of Langmuir Waves with Whistler Waves in the Solar Wind

Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations, a theory is formulated to describe the nonlinear coupling of Langmuir waves and whistler waves. It is shown that a Langmuir wave can interact nonlinearly with a whistler wave to produce either right-hand or left-hand circularly polarized electromagnetic waves. Nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind. Numerical examples of whistler frequency, nonlinear growth rate and modulation frequency for solar wind parameters are calculated.

Stimulated scattering of high-power radio waves in multi-component collisional plasmas

Abstract The nonlinear coupling of intense radio waves with the low-frequency electrostatic perturbations of multi-component collisional plasmas is considered. Assuming the presence of two distinct groups of electrons and singly charged ions, we obtain equations for the radio wave sidebands and plasma slow motions that are driven by the combined effects of the radiation pressure and the differential Joule heating of the electrons. The mode coupling equations are useful for studying various types of stimulated scattering instabilities and envelope soliton formation. The relevance of our investigation to the simultaneous generation of density and temperature fluctuations by high-power radio waves is pointed out.

Evidence for nonlinear coupling of planetary waves and tides in the Antarctic mesopause

Analyses of hourly‐mean meridional and zonal winds near 95 km, observed with the meteor radar system at Molodezhnaya station (68°S, 45°E) during 1990, reveal the presence of long‐period (2–18 day) waves with dominant periods corresponding to those of Rossby normal modes modified by mean zonal winds. Time–varying analyses indicate that although significant contributions at planetary wave periods persist with nearly constant periods for intervals of days to weeks, temporal variability of these periods is observed over longer intervals. Tidal motions, which mainly consist of the semidiurnal and the diurnal periods, demonstrate considerable modulation of their amplitudes that vary with time. The observed tidal amplitude modulations are investigated through bispectral analyses. The results of these analyses suggest nonlinear interactions of quadratic form between oscillations with periods in the range of 2 to 19 days and the diurnal and semidiurnal tides at various intervals during 1990.

Radiation of whistlers by the ion‐acoustic turbulence in the ionosphere

The generation of whistlers in the ionosphere due to the nonlinear coalescence of ion‐acoustic waves is analyzed by means of the weak turbulence approach. The ion‐acoustic turbulence is supposed to be driven by field‐aligned currents or/and the nonlinear coupling of Langmuir waves generated in an unstable beam‐plasma system. The spectral power of whistlers radiated by the ion‐acoustic turbulence is evaluated with special regard to small‐scale auroral events, artificial injections of an electron beam, and the tethered satellite system. In particular, this mechanism of whistler radiation can contribute to the low‐frequency part of the auroral hiss.

Nonlinear coupling of lower hybrid waves to the kinetic low‐frequency plasma response in the auroral ionosphere

A hybrid kinetic‐fluid model is developed which is relevant to lower hybrid spikelets observed in the topside auroral ionosphere [Vago et al., 1992; Eriksson et al., 1994]. In contrast to previous fluid models [Shapiro et al., 1995; Tam and Chang, 1995; Seyler, 1994; Shapiro et al., 1993] our linear low frequency plasma response is magnetized and kinetic. Fluid theory is used to incorporate the nonlinear wave coupling. Performing a linear stability analysis, we calculate the growth rate for the modulational instability, driven by a lower hybrid wave pump. We find that both the magnetic and kinetic effects inhibit the modulational instability.

Fine structure in plasma waves and radiation near the plasma frequency in Earth's foreshock

Novel observations are presented of intrinsic fine structure in the frequency spectrum of electromagnetic (EM) radiation and plasma waves near the electron plasma frequency fp during a period of unusually high interplanetary magnetic field strength. Measured using the wideband receiver on the ISEE 1 spacecraft, fine‐structured emissions are observed both in the solar wind and the foreshock. The fine structure is shown to correspond to emissions spaced above fp near half harmonics of the electron cyclotron frequency fce, i.e., near fp + nfce/2. These appear to be the first space physics observations of emissions spaced by fce/2. Indirect but strong arguments are used to discriminate between EM and electrostatic (ES) signals, to identify whether ISEE 1 is in the solar wind or the foreshock, and to determine the relative frequencies of the emissions and the local fp. The data are consistent with generation of the ES and EM emissions in the foreshock, with subsequent propagation of the EM emissions into the solar wind. It remains possible that some emissions currently identified as ES have significant EM character. The ES and EM emissions often merge into one another with minimal changes in frequency, arguing that their source regions and generation mechanisms are related and imposing significant constraints on theories. The fce/2 ES and EM fine structures observed may be intrinsic to the emission mechanisms or to superposition of two series of signals with fce spacing that differ in starting frequency by fce/2. Present theories for nonlinear wave coupling processes, cyclotron maser emission, and other linear instability processes are all unable to explain multiple EM and/or ES components spaced by ∼fce/2 above fp for fp/fce ≫ 1 and typical foreshock beam parameters. Suitable avenues for further theoretical research are identified. Empirically, the observed fine structures appear very similar to those in split band and multiple‐lane type II solar radio bursts; interpretation of both these type II fine structures in terms of fce/2 splitting is suggested, thereby supporting and generalizing a suggestion by Wild (1950). A possible application to continuum radiation is mentioned. The ubiquity of these fine structures in the Earth's fp radiation and foreshock waves remains unknown. Only the ISEE 1 wideband receiver has sufficient frequency resolution (≲ 100 Hz) to perform a dedicated search. Further study of the ubiquity of these fine structures, of how reliably the splitting corresponds to fce/2 and of the other interpretations above is necessary.

Wave collapse at the lower-hybrid resonance

The modulational instability and collapse of waves in the vicinity of the lower-hybrid resonance including both magnetosonic and lower-hybrid waves are investigated by analytical and numerical methods. The mechanism leading to the modulational instability is the nonlinear coupling of lower-hybrid waves with the much lower-frequency quasineutral density perturbations via the ponderomotive force. The result is a filamentation of the high-frequency field producing elongated, cigar-shaped nonlinear wave packets aligned along the magnetic field with the plasma expelled outside (cavities). The analytical self-similar solutions describing cavity collapse are obtained and compared with the results of numerical simulation for both two- and three-dimensional cavity geometries. It is shown that in three-dimensional solutions the transverse, with respect to the magnetic field, contraction remains prevailing. The possibility of ion acceleration as the result of the lower-hybrid collapse is discussed and detailed comparison is made with the observations of the phenomena in the auroral ionosphere.

Experiments on the nonlinear stages of excited and natural planar jet shear layer transition

An experimental investigation focusing on the nonlinear stages of planar jet shear layer transition is presented. Experimental results for transition under both “natural” and low level artificial forcing conditions are presented and compared. The local spectral dynamics of the jet shear layer is modeled as a nonlinear system based upon a frequency domain, second-order Volterra functional series representation. The local linear and nonlinear wave coupling coefficients are estimated from time-series streamwise velocity fluctuation data. From the linear coupling coefficient, the mean dispersion characteristics and spatial growth rates may be obtained. With the estimation of the nonlinear power transfer function, the total, linear and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and linear-quadratic coupling bicoherency, the local system output power may be completely characterized and the effect of nonlinearity on local mean flow distortion assessed. Particular attention is focused upon quantifying the linear and nonlinear power transfer that characterizes the different stages of the jet shear layer transition for both natural and excited flows. The quadratic power transfer that occurs with deviation from the perfect resonant wavenumber matching condition is clarified as is the dynamic mechanism of subharmonic resonance. The mechanism of spectral broadening is described and contrasted for natural and artificially excited flows.

Nonlinear wave coupling and subharmonic resonance in planar jet shear layer transition

An experimental investigation of the nonlinear spectral development associated with the transition of an initially laminar planar jet shear layer is presented. The local shear layer spectral dynamics are modeled as a nonlinear system containing both linear and quadratically nonlinear system elements. A novel digital signal processing technique is applied which allows the linear and quadratically nonlinear wave coupling coefficients that characterize the local spectral dynamics to be estimated directly from time-series velocity fluctuation data. The method utilized is noniterative and explicitly includes fourth-order spectral moments. From the linear coupling coefficient, the local spatial growth rate and dispersion relation may be obtained. Of particular interest in the work reported is the associated nonlinear wave coupling coefficient which provides a measure of the efficiency of local nonlinear three-wave coupling. These show that the jet shear layer exhibits a strong preference for difference mode interactions. With the estimation of the related nonlinear power transfer function, the total, linear, and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and local linear–quadratic coupling bicoherency, the local nonlinear spectral dynamics of the flow may be completely and unambiguously quantified. Particular emphasis is placed upon discerning the mechanism which gives rise to subharmonic resonance with the fundamental. Results show that the amplification of the subharmonic occurs via a parametric resonance with the fundamental rather than by direct quadratic difference interaction. That is, the subharmonic is boosted by a weakly nonlinear mechanism involving a linear growth rate modification due to a resonant phase lock with the fundamental instability.

Anomalous absorption of electromagnetic radiation

Transverse structure in a plasma at the critical layer can increase the coupling between electromagnetic and electrostatic waves and lead to enhanced absorption of the radiation. Simulations show cases of nearly 90% absorption of the incident energy. A ripple across the density gradient acts to focus the incoming electromagnetic radiation in the lower density regions coupling it to electrostatic modes through the transverse density gradients. A simple model of the absorption shows good agreement with the scalings observed in the computer simulations. Part of the reflected radiation is side scattered at ±nkt, where kt is the wave number of the transverse structure. This can reduce the directly backscattered radiation to 0.6% of the incident energy. Nonlinear coupling of the electrostatic waves leads to radiation at twice the incident frequency.