Nonlinear Wave Coupling Research Articles

Nonlinear interaction of the fast magnetosonic wave with the extraordinary mode laser and ion-scaled turbulence generation in the magnetized plasma

This study introduces a nonlinear wave-wave coupling model to understand the nature of the turbulence generation at the ion scale observed in the interaction of high-intensity laser with plasma. For this nonlinear coupling of waves, the fast magnetosonic wave and the extraordinary mode laser are taken into account, along with the nonlinear ponderomotive force. The model dynamical equations have been developed for the extraordinary mode laser and the fast magnetosonic wave. Laboratory simulations have been employed to solve the obtained model equations utilizing the finite difference and pseudo-spectral methods. The simulation results show the initiation of the nonlinear progression of the laser beam at an early time and its turbulent nature at a later time. The background density perturbation, along with the cavity and hump caused by the ponderomotive force, has also been studied. The simulation results demonstrate that the propagation angle of the fast magnetosonic wave affects the magnitudes of the localization of the laser beam (pump wave) and the perturbed background density. The turbulent power spectra (ensemble-averaged) have also been studied for the different propagation angles of the fast magnetosonic wave. The turbulent spectra demonstrate that the plasma turbulence is MHD-type at small-scale lengths and ion-dominated at larger-scale lengths. This study also observed that the simulation results have some resemblance with the experimental results reported by Chatterjee et al.12 in the intense laser-plasma interaction experiment at a laboratory astrophysical scale.

A fermi acceleration model to study the electron acceleration in laser-produced plasma with localized structures formation and turbulence generation

This investigation presents a model based on the nonlinear coupling of waves for studying electron acceleration in laser-produced plasma. The impact of the localized structures formation and turbulence generation on electron acceleration is investigated via a second-order Fermi acceleration mechanism. For this purpose, the dynamical coupled equations of the extraordinary mode laser and the upper hybrid wave are formulated by taking into account relativistic and ponderomotive nonlinearity. These coupled equations are solved by laboratory simulations using pseudo-spectral and finite difference methods. The simulation results show the turbulent wavenumber spectrum associated with the localization of the laser beam. The power-law scaling of turbulence generation has been utilized to study the formation of the thermal tail of energetic electrons, which may be responsible for the acceleration of the electrons. A fractional diffusion method has been exploited to determine electron acceleration. This study also provides a simplified model for a better understanding of the nonlinear progression of the laser beam during propagation inside the magnetized plasma.

Experimental study on the effect of an oyster reef on the nonlinear characteristics of irregular waves

As a “marine ecological engineer”, the oyster reefs not only perform important ecological functions, but also reduce the damage caused by waves to protective structures such as seawalls. However, oyster reefs in shallow water change the nonlinear characteristics of waves and affect sediment transport and coastal evolution. Based on Fourier spectrum and analysis of Wavelet Transform, the influence of artificial bag oyster reefs on the energy and nonlinear phase coupling of irregular waves are studied through physical experiment. The results show that oyster reefs have a substantial effect on the energy of primary harmonic, which transfer to higher harmonics through triad interactions, and a considerable reduction in primary harmonic energy and an increase in higher harmonics energy are reflected in the energy spectra. The transmission spectrum behind the oyster reefs shows three peaks at primary, secondary and third harmonics. The bicoherence spectrum indicates that the peaks at secondary and third harmonics mainly result from the self-coupling of the primary harmonics and phase coupling between the primary and secondary harmonics respectively. As the water depth increases, the degree of nonlinear coupling between wave components decreases, which leads to the energy of wave components at different frequencies increases. With increasing top width, the length of the shoaling region increases, and the growth of triad nonlinear interactions are observed in wavelet-based bicoherence spectra, resulting in the spectral peak energy decreasing while the secondary harmonics energy increasing in the spectrum. Finally, the potential application of an ecological system composed by “oyster reefs + mangroves” is discussed. As the effect of water depth on wave energy is much greater than that of top width, in artificial oyster reef construction, it is recommended that keep the oyster reefs non-submerged in terms of wave dissipation. Further studies should take the dynamic growth effect of oyster reefs into account.

The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.

Floquet-Mode Traveling-Wave Parametric Amplifiers

Simultaneous ideal quantum measurements of multiple single-photon-level signals would advance applications in quantum information processing, metrology, and astronomy, but require the first amplifier to be simultaneously broadband, quantum limited, and directional. However, conventional traveling-wave parametric amplifiers support broadband amplification at the cost of increased added noise and are not genuinely directional due to non-negligible nonlinear backward wave generation. In this work, we introduce a new class of amplifiers which encode the information in the Floquet modes of the system. Such Floquet mode amplifiers prevent information leakage and overcome the trade-off between quantum efficiency (QE) and bandwidth. Crucially, Floquet mode amplifiers strongly suppress the nonlinear forward-backward wave coupling and are therefore genuinely directional and readily integrable with qubits, clearing another major obstacle towards broadband ideal quantum measurements. Furthermore, Floquet mode amplifiers are insensitive to out-of-band impedance mismatch, which otherwise may lead to gain ripples, parametric oscillations, and instability in conventional traveling-wave parametric amplifiers. Finally, we show that a Floquet mode Josephson traveling-wave parametric amplifier implementation can simultaneously achieve $>\!20\,$dB gain and a QE of $\eta/\eta_{\mathrm{ideal}}\!> 99.9\%$ of the quantum limit over more than an octave of bandwidth. The proposed Floquet scheme is also widely applicable to other platforms, such as kinetic inductance traveling-wave amplifiers and optical parametric amplifiers.

Plasma Emission versus Electron Cyclotron Maser Emission due to Power-law Energetic Electrons in Differently Magnetized Coronal Plasmas

Abstract By using self-consistent 2.5-dimensional particle-in-cell simulations, we study the excitation efficiency of electromagnetic waves by power-law energetic electrons with an anisotropic pitch-angle velocity distribution, which can simultaneously trigger the Langmuir and electron cyclotron maser instabilities, in differently magnetized coronal plasmas. It is found that the (transverse) electromagnetic waves can be excited much more efficiently in the case of strongly magnetized plasmas with ω ce > ω pe than that of weakly magnetized plasmas with ω ce < ω pe, where ω ce and ω pe are the electron cyclotron frequency and the electron plasma frequency, respectively. In particular, in a weakly magnetized plasma the electromagnetic wave is hardly excited effectively via the nonlinear coupling of Langmuir waves; although the Langmuir waves can be generated by the power-law energetic electrons, implying that the so-called plasma emission does not effectively work. These results can be helpful for us to better understand the physical mechanism of solar radio bursts.

Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space

<p style='text-indent:20px;'>In this paper, we study the global existence and pointwise behavior of classical solution to one dimensional isentropic Navier-Stokes equations with mixed type boundary condition in half space. Based on classical energy method for half space problem, the global existence of classical solution is established firstly. Through analyzing the quantitative relationships of Green's function between Cauchy problem and initial boundary value problem, we observe that the leading part of Green's function for the initial boundary value problem is composed of three items: delta function, diffusive heat kernel, and reflected term from the boundary. Then applying Duhamel's principle yields the explicit expression of solution. With the help of accurate estimates for nonlinear wave coupling and the elliptic structure of velocity, the pointwise behavior of the solution is obtained under some appropriate assumptions on the initial data. Our results prove that the solution converges to the equilibrium state at the optimal decay rate <inline-formula><tex-math id="M1">\begin{document}$ (1+t)^{-\frac{1}{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M2">\begin{document}$ L^\infty $\end{document}</tex-math></inline-formula> norm.</p>

A nonlinear wave coupling algorithm and its programing and application in plasma turbulences

The fully developed turbulence can be regarded as a nonlinear system, with wave coupling inside, which causes the nonlinear energy to transfer, and drives the turbulence to develop further or be suppressed. Spectral analysis is one of the most effective methods to study turbulence system. In order to apply it to the study of the nonlinear wave coupling process of edge plasma turbulence, an efficient algorithm based on spectral analysis technology is proposed to solve the nonlinear wave coupling equation. The algorithm is based on a mandatory temporal static condition with the nonideal spectra separated from the ideal spectra. The realization idea and programing flow are given. According to the characteristics of plasma turbulence, the simulation data are constructed and used to verify the algorithm and its implementation program. The simulation results and experimental results show the accuracy of the algorithm and the corresponding program, which can play a great role in the studying the energy transfer in edge plasma turbulences. As an application, the energy cascade analysis of typical edge plasma turbulence is carried out by using the results of a case calculation. Consequently, a physical picture of the energy transfer in a kind of fully developed turbulence is constructed, which confirms that the energy transfer in this turbulent system develops from lower-frequency region to higher-frequency region and from linear growing wave to damping wave.

Nonlinear evolution of localized structures and turbulent magnetic field amplification by extraordinary laser beam in laser produced plasmas

In the present investigation, the nonlinear coupling of waves is evaluated to understand the turbulent magnetic field in the laser-produced plasma. The model equations are set up for the extraordinary (x-mode) laser and upper hybrid oscillations, incorporating the relativistic electron mass variation and the nonlinear ponderomotive force. The upper hybrid oscillations are excited due to the nonlinear ponderomotive force exerted by the x-mode laser. The nonlinear coupled system of x-mode laser and the upper hybrid oscillations were simulated numerically. Simulation results depict the evolution of localized structures with time. The ensemble-averaged turbulent power spectrum is obtained through numerical simulations. Furthermore, the frequency spectra associated with upper hybrid oscillation lie in the terahertz (THz) frequency range. A semi-analytical approach in the paraxial approximation has been studied to get a better perspective of the field localization process. Such studies of nonlinear wave-wave interaction are crucial to understand the turbulent magnetic field generation relating to various laboratory and astrophysical scenarios.

Particle-in-cell simulation of plasma emission in solar radio bursts

Aims. The present study aims to shed light on our understanding of the radiation processes of solar radio bursts associated with nonthermal electron propagation in the corona and interplanetary space. Methods. We performed 2.5-dimensional particle-in-cell (PIC) simulations to investigate the plasma emission excited by a relativistic electron beam using different pitch angles in the magnetized plasma. Results. Langmuir waves at the fundamental and harmonic frequencies were excited via the energy dissipation of the electron beam. For the first time, the backward Langmuir waves up to the third harmonic frequencies were reproduced in the cases of large pitch angles, likely arising from the relecting and scattering of density fluctuations to the Langmuir waves during electrom beam-plasma interaction. Electromagnetic (EM) waves were generated via the mode conversion of electrostatic (ES) waves and the nonlinear wave coupling. Specifically, the harmonic EM emission comes from the coupling of forward and backward Langmuir waves, namely, L + L′ → 2H, while the higher harmonic EM emissions generally come from the coupling of the Langmuir wave and lower-order harmonic EM wave, namely, L + (n − 1)H → nH. When the electron beam exhibits a large pitch angle, another possible mechanism for the third harmonic EM emission might be the coalescence of three ES waves, namely, L + L′ + L″ → 3H.

Fast dynamics of radiofrequency emission in FTU plasmas with runaway electrons

Radiofrequency emission in the 0.4–3 GHz range from FTU tokamak in presence of runaway electrons (REs) has been measured in various plasma regimes. Rapid emission bursts associated with enhanced RE pitch-angle scattering reveal kinetic instabilities affecting evolution of the RE population from the buildup phase. Such measurements also provide a sensitive monitor for instabilities during early RE formation. The leading edge of radio bursts is much shorter than interleaving periods of low emission; spectral broadening during growth indicates nonlinear wave coupling as an explanation for the observed intermittency. Both broadband and coherent spectra have been observed. Radio emission disappears at the beginning of post-disruption RE plateaus, and subsequently reappears in the shape of very intense bursts accompanied by macroscopic magnetic perturbations.

Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma

Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.

Two‐dimensional drift solitary structures in inhomogeneous magnetized OH ion plasmas with generalized (r, q) distributed electrons

AbstractIn this paper, the effect of generalized (r, q) distributed electrons on the linear and nonlinear coupling of drift and ion acoustic waves in a nonuniform plasma containing Hydrogen and Oxygen ions is investigated. In the linear regime, it is observed that increasing the percentage of flat‐topped (i.e. r > 0) electrons enhances the frequency of the coupled drift‐ion acoustic waves, whereas the increasing values of the spectral index q mitigates it. In the nonlinear regime, one‐ and two‐dimensional Korteweg de Vries‐like and Kadomtsev‐Petviashvili‐like equations are derived and their solutions are plotted for different ratios of ion number densities and for different values of double spectral indices r and q of the generalized distribution of electrons. It is found that only rarefactive structures exist for two‐dimensional solitons, however, both rarefactive and compressive structures are observed for the one‐dimensional case. The limiting cases of kappa and Maxwellian distributions are also discussed and their comparison with the generalized (r, q) distribution is thoroughly investigated. Spatial scales for the formation of rarefactive and compressive solitary structures are also discussed with reference to the changing electron distribution functions. The possible applications of the present study are also spelled out with special reference to space plasmas.

Curry-Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems.

The routes to chaos play an important role in predictions about the transitions from regular to irregular behavior in nonlinear dynamical systems, such as electrical oscillators, chemical reactions, biomedical rhythms, and nonlinear wave coupling. Of special interest are dissipative systems obtained by adding a dissipation term in a given Hamiltonian system. If the latter satisfies the so-called twist property, the corresponding dissipative version can be called a "dissipative twist system." Transitions to chaos in these systems are well established; for instance, the Curry-Yorke route describes the transition from a quasiperiodic attractor on torus to chaos passing by a chaotic banded attractor. In this paper, we study the transitions from an attractor on torus to chaotic motion in dissipative nontwist systems. We choose the dissipative standard nontwist map, which is a non-conservative version of the standard nontwist map. In our simulations, we observe the same transition to chaos that happens in twist systems, known as a soft one, where the quasiperiodic attractor becomes wrinkled and then chaotic through the Curry-Yorke route. By the Lyapunov exponent, we study the nature of the orbits for a different set of parameters, and we observe that quasiperiodic motion and periodic and chaotic behavior are possible in the system. We observe that they can coexist in the phase space, implying in multistability. The different coexistence scenarios were studied by the basin entropy and by the boundary basin entropy.

Harmonic Radio Emission in Randomly Inhomogeneous Plasma

Abstract In the present paper, we describe a theoretical model of the generation of harmonic emissions of type III solar radio bursts. The goal of our study is to fully take into account the most efficient physical processes involved in the generation of harmonic electromagnetic emission via nonlinear coupling of Langmuir waves in randomly inhomogeneous plasma of solar wind ( ). We revisit the conventional mechanism of coalescence of primarily generated and back-scattered Langmuir waves in quasihomogeneous plasma. Additionally, we propose and investigate another mechanism that generates harmonic emission only in a strongly inhomogeneous plasma: the nonlinear coupling of incident and reflected Langmuir waves inside localized regions with enhanced plasma density (clumps), in the close vicinity of the reflection point. Both mechanisms imply the presence of strong density fluctuations in plasma. We use the results of a probabilistic model of beam–plasma interaction and evaluate the efficiency of energy transfer from Langmuir waves to harmonic emission. We infer that harmonic emissions from a quasihomogeneous plasma are significantly more intense than found in previous studies. The efficiency of Langmuir wave conversion into electromagnetic harmonic emission is expected to be higher at large heliospheric distances for the mechanism operating in quasihomogeneous plasma and at small heliocentric distances for the one operating in inhomogeneous plasma. The evaluation of emission intensity in quasihomogeneous plasma may also be applied for type II solar radio bursts. The radiation pattern in both cases is quadrupolar, and we show that emission from density clumps may efficiently contribute to the visibility of harmonic radio emission.

Observation of infragravity wave processes near the coastal cliffs of Chabahar (Gulf of Oman)

This study analyzed the characteristics of infragravity waves (hereafter IGWs) based on field observations collected near the plunging cliffs of Chabahar bay, Iran. Observations were made near Chabahar city during the summer monsoon season of 2018. The wave climate included two different durations of sea and swell predominance, with a maximum wave height reaching 2.5 m. Concurrent with the duration of the sea predominance, the ratio of IGW to swell wave height had an insensitive fluctuation against tidal variations, while this ratio had a strong negative correlation with tidal level during the high swell condition. The investigation of directional wave energy distribution revealed two correlated trends of shoreward and seaward IGWs with the wave regime.Larger values of the IGW reflection coefficients were observed during high sea wave conditions compared with high swell conditions. The IGW reflection coefficients decreased against swell energy growth with a logarithmic trend. The bound IGW energy fraction was studied using bispectral analysis. It is demonstrated that the maximum values of this parameter corresponded to high swell waves observed within low ebbs of the spring tide. The insignificant values of bound IGW energy fraction and the non-extended surf-zone revealed that most of the released IGWs originated from offshore and intermediate water depths. In addition, it was revealed that the inverse tidal trend of normalized IGW by swell height was due to bound IGW enhancement during ebb periods as a result of the nonlinear coupling of swell waves.

High-dimensional orbital angular momentum multiplexing nonlinear holography

Nonlinear holography has been identified as a vital platform for optical multiplexing holography because of the appearance of new optical frequencies. However, due to nonlinear wave coupling in nonlinear optical processes, the nonlinear harmonic field is coupled with the input field, laying a fundamental barrier to independent control of the interacting fields for holography. We propose and experimentally demonstrate high-dimensional orbital angular momentum (OAM) multiplexing nonlinear holography to overcome this problem. By dividing the wavefront of the fundamental wave into different orthogonal OAM channels, multiple OAM and polarization-dependent holographic images in both the fundamental wave and second-harmonic wave have been reconstructed independently in the spatial frequency domain through a type-II second harmonic generation process. Moreover, this method can be easily extended to cascaded χ2 nonlinear optical processes for multiplexing in more wavelength channels, leading to potential applications in multicasting in optical communications, multiwavelength display, multidimensional optical storage, anticounterfeiting, and optical encryption.

Cold-hot coupled waves in a flowing magnetized plasma

Nonlinear coupling of cold and hot waves in a flowing magnetized plasma is analyzed with the Vlasov equation. An analytical solution is obtained for cold waves of a small amplitude (weak flow) and a long wavelength. The distribution function is obtained by integrating the kinetic equation along a perturbed phase-space trajectory for a time-varying plasma flow. The kinetic description presents a generalized dispersion relation that involves resonances depending on cold and hot wave dispersions. Coherent fluid motion leads to radiation peaks in addition to the cyclotron harmonics, where the wavenumber of the cold wave determines the peak frequencies. The peaks appear narrow when the wave propagates perpendicular to the time-averaged flow while they become broad due to the Doppler effect when the wave propagates parallel to the flow. Fully kinetic particle-in-cell simulations corroborate the theoretical predictions. The dispersion relation and resulting wave spectra provide information about plasma parameters and flow properties.

Nonlinear coupling of electromagnetic and electron acoustic waves in multi-species degenerate astrophysical plasma

Nonlinear wave-coupling is studied in a multispecies degenerate astrophysical plasma consisting of two electron species (at different temperatures): a highly degenerate main component plus a smaller classical relativistic flow immersed in a static neutralizing ion background. It is shown that the high frequency electromagnetic waves through their strong nonlinear interactions with the electron-acoustic waves [sustained by a multielectron component (degenerate) plasma surrounding a compact astrophysical object] can scatter to lower frequencies so that the radiation observed faraway will be spectrally shifted downward. It is also shown that, under definite conditions, the electromagnetic waves could settle into stationary solitonic states. It is expected that the effects of such structures may persist as detectable signatures in forms of modulated micropulses in the radiation observed far away from the accreting compact object. Both these effects will advance our abilities to interpret the radiation coming out of the compact objects.

LPSE: A 3-D wave-based model of cross-beam energy transfer in laser-irradiated plasmas

The new component of the “laser–plasma simulation environment” (LPSE) described here is a practical numerical model that solves the coupled vector equations for the propagation of nearly monochromatic, coherent, electromagnetic waves in inhomogeneous unmagnetized plasmas. It operates efficiently in the numerically challenging semiclassical regime where characteristic plasma scale lengths are many times greater than the wavelength of the light and solutions are highly oscillatory. Solutions can be obtained in one, two, or three spatial dimensions and time. The model includes the effects of nonlinear coupling of electromagnetic waves to the low-frequency plasma perturbations (i.e., ion-acoustic response) that are responsible for stimulated Brillouin scattering. Induced plasma perturbations are assumed to be imposed on a prescribed large-scale inhomogeneous background that includes spatially varying plasma density and flow. Our code is directly relevant to the problem of cross-beam energy transfer in laser-driven inertial confinement fusion. It may also be applicable in other areas where eikonal solutions of multicomponent wave equations (or coupled wave equations) are insufficient, such as optical scattering from ultrasound, electron dynamics in quantum devices or in nanoscale light–matter interactions.