Three-wave Interaction Processes Research Articles

Random wavenumber and nonlinear parametric effect of speckle field

Speckle field is a relatively common phenomenon. But the speckle has special application value in nonlinear optical domain because it can be used to suppress different nonlinear processes that are caused by high power laser. To enhance the suppression capability, it is necessary to reveal the basic mechanism of the speckle parameter nonlinear optical interaction process. In this work, the coupling wave equation under the wave number mismatch condition is used to analyze the parameter process of speckles field. The solving process of the coupling wave equation is introduced in detail. And the wave number or phase matching condition is fully discussed. Furthermore, the threshold of the nonlinear gain is analyzed when the wave number does not fully meet the matching condition. To describe the solution of the coupling wave equation more clearly, the undetermined coefficient of the exact analytical solution is discussed. Since the boundary field will affect the confirmation of the undetermined coefficient, the characteristic of boundary field should be analyzed first. The nonlinear process of the speckle field is a three-wave interaction process. The different boundary conditions will affect the three-wave interaction process. And it is found that if the complex amplitudes of the three waves at the boundary are not zero, the undetermined coefficient will be changed with the phrase parameters of the three waves. To achieve the maximum value, the boundary waves must meet the phase matching condition. The wave number of the speckle filed is not an invariant, because of its random distribution characteristic. Therefore, during the analysis of the three-wave interaction process, the segment handling method is used to ensure the effective solving of the first order coupling wave equation. On the other hand, the randomly fluctuation of the wave number destroys the phase matching condition of the boundary. It is just through the basic mechanism that the speckle field can be used to suppress the nonlinear gain of high-power optical field. Both the theoretical analyses and the numerical calculation results show that the speckle field has good suppression effect for some typical nonlinear parameter process, such as stimulated Brillouin scattering.

Simulation of parametric decay instability excited by oscillating pump near lower hybrid frequency

Parametric decay instability of lower hybrid waves plays an important role in plasma heating. Simulation of such instability requires inclusion of both electron and ion kinetics with a realistic mass ratio. In this work, the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model is used to study parametric instabilities in uniform, magnetized plasmas. A pump electric field near the lower hybrid frequency is imposed, which is treated in the dipole approximation. Three types of parametric decay processes are obtained, including purely growing modulational instability, resonant decay instability, and non-resonant decay instability. Dependences of parametric growth rates on the wavenumber, pump strength, and pump frequency are systematically investigated. The simulation results agree well with those in the linear growth stage of parametric decay instability obtained in an existing theory. Whether electron or ion nonlinearity dominates in the parametric decay process is assessed, and the importance of the electron E×B drift in the three-wave interaction process is confirmed.

Thermo-Optic Effects in Congruent-LiTaO 3 Based Continuous-Wave Optical Parametric Oscillator

We present an experimental study on single-frequency, singly-resonant optical parametric oscillator (SRO) comprised of 50 mm long congruently-grown, 8-mol%-doped, periodically-poled LiTaO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (MgO:cPPLT) crystal. The SRO is pumped by a single-frequency, fiber laser pumped green laser. Our observations reveal that the SRO output (idler) scales linearly with the pump power ( P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ) near the SRO threshold ( P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p(th)</sub> ). However, the SRO idler power ( P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ) exhibits strong saturation at pump power ≈ 1.5P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p(th)</sub> which eventually switches-off the SRO operation on further pump-power enhancement. By coarsely tuning the MgO:cPPLT crystal temperature from 50 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> C to 170 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> C, the SRO idler wavelength is varied from 1810-1920 nm wavelength band. A maximum idler power P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =583 mW was obtained when the input pump power was ≈ 3.1 W. The idler power saturation is accompanied by discernible distortion in idler beam profile. An early onset of saturation in MgO:cPPLT is essentially a consequence of strong linear absorption exhibited by MgO:cPPLT at pump wavelength, its high thermo-optic coefficient as well as low thermal conductivity. The results are theoretically analyzed by solving the heat conduction equation which provides a deeper insight about the impact of pump-induced thermo-optic effects on a three-wave interaction process.

High-power terahertz emission from a plasma penetrated by counterstreaming different-size electron beams

It is found that multi-cycle pulses of high-power coherent terahertz radiation can be efficiently generated in a plasma by counterstreaming long-pulse electron beams driving potential plasma waves via the two-stream instability. Instead of the well-known three-wave interaction processes between oblique beam-driven modes, we propose to generate electromagnetic radiation near the doubled plasma frequency due to the novel and much more efficient mechanism based on the head-on collision of longitudinal plasma waves with mismatching potential profiles. It is shown that this radiation mechanism can be implemented experimentally either by the collision of low-density electron beams with different transverse sizes or by the counter injection of denser equal-size beams unstable against filamentation perturbations. Particle-in-cell simulations for kiloampere electron beams capable of focusing into millimeter-scale sizes demonstrate the possibility to reach the high efficiency of beams-to-THz power conversion (3%–7%), which opens the path to gigawatt-class THz sources with a narrow spectral line.

Generation of THz radiation by parametric coupling of laser and Trivelpiece–Gould mode

A scheme to generate terahertz radiation is proposed, wherein the high power, perpendicular-extraordinary laser pump (X-mode) (ω0) parametrically decays into the Trivelpiece-Gould (TG) (ω1) mode and kinetic Alfvén wave (ω2) at an oblique angle with the external magnetic field. The nonlinear interaction amongst the three interacting waves leads to the existence of quasi-static ponderomotive force. Furthermore, under the influence of this force, electrons acquire nonlinear oscillatory velocity. A strong transient current is generated by the nonlinear coupling of laser velocity and TG density perturbation. This nonlinear current drives a wave, whose frequency is obtained in the terahertz range (ω2=ω0−ω1) after optimizing various laser-plasma parameters. For the resonant excitation of the wave, the requisite phase matching condition is shown by modelling the parallelogram, which follows the principle of conservation of energy and momentum simultaneously. The coupling coefficients for the three-wave interaction process along with the growth rate of decay instability are investigated.

Complete Hamiltonian formalism for inertial waves in rotating fluids

A complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluids. Resonance three-wave interaction processes – decay instability and confluence of two waves – are shown to play a key role in the weakly nonlinear dynamics and statistics of inertial waves in the rapid rotation case. Future applications of the Hamiltonian approach to inertial wave theory are investigated and discussed.

A new decay channel for upper-hybrid waves

We look here at a three-wave interaction process involving only electrostatic waves in an electron plasma with stationary ions. Special attention is given to the case with an upper-hybrid wave as a pump wave, where a new decay channel is pointed out. The corresponding growth rate is calculated.

Non-linear Alfvén wave interaction leading to resonant excitation of an acoustic mode in the laboratorya)

The nonlinear three-wave interaction process at the heart of the parametric decay process is studied by launching counter-propagating Alfvén waves from antennas placed at either end of the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)]. A resonance in the beat wave response produced by the two launched Alfvén waves is observed and is identified as a damped ion acoustic mode based on the measured dispersion relation. Other properties of the interaction including the spatial profile of the beat mode and response amplitude are also consistent with theoretical predictions for a three-wave interaction driven by a nonlinear ponderomotive force. A simple damped, driven oscillator model making use of the MHD equations well-predicts most of the observations, but the width of the resonance curve is still under investigation.

Weak turbulence theory for rotating magnetohydrodynamics and planetary flows

AbstractA weak turbulence theory is derived for magnetohydrodynamics (MHD) under rapid rotation and in the presence of a uniform large-scale magnetic field which is associated with a constant Alfvén velocity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\boldsymbol {b}}_{{0}}$. The angular velocity ${\boldsymbol{\Omega}}_{{0}}$ is assumed to be uniform and parallel to ${\boldsymbol {b}}_{{0}}$. Such a system exhibits left and right circularly polarized waves which can be obtained by introducing the magneto-inertial length $d \equiv b_0/\varOmega _0$. In the large-scale limit ($kd \to 0$, with $k$ being the wavenumber) the left- and right-handed waves tend to the inertial and magnetostrophic waves, respectively, whereas in the small-scale limit ($kd \to + \infty $) pure Alfvén waves are recovered. By using a complex helicity decomposition, the asymptotic weak turbulence equations are derived which describe the long-time behaviour of weakly dispersive interacting waves via three-wave interaction processes. It is shown that the nonlinear dynamics is mainly anisotropic, with a stronger transfer perpendicular than parallel to the rotation axis. The general theory may converge to pure weak inertial/magnetostrophic or Alfvén wave turbulence when the large- or small-scale limits are taken, respectively. Inertial wave turbulence is asymptotically dominated by the kinetic energy/helicity, whereas the magnetostrophic wave turbulence is dominated by the magnetic energy/helicity. For both regimes, families of exact solutions are found for the spectra, which do not correspond necessarily to a maximal helicity state. It is shown that the hybrid helicity exhibits a cascade whose direction may vary according to the scale $k_f$ at which the helicity flux is injected, with an inverse cascade if $k_fd &lt; 1$ and a direct cascade otherwise. The theory is relevant to the magnetostrophic dynamo, whose main applications are the Earth and the giant planets, such as Jupiter and Saturn, for which a small (${\sim }10^{-6}$) Rossby number is expected.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Nonlinear Excitation of Acoustic Modes by Large-Amplitude Alfvén Waves in a Laboratory Plasma

The nonlinear three-wave interaction process at the heart of the parametric decay process is studied by launching counterpropagating Alfvén waves from antennas placed at either end of the Large Plasma Device. A resonance in the beat wave response produced by the two launched Alfvén waves is observed and is identified as a damped ion acoustic mode based on the measured dispersion relation. Other properties of the interaction including the spatial profile of the beat mode and response amplitude are also consistent with theoretical predictions for a three-wave interaction driven by a nonlinear ponderomotive force.

NONLINEAR WAVE INTERACTIONS AS EMISSION PROCESS OF TYPE II RADIO BURSTS

The emission of fundamental and harmonic frequency radio waves of type II radio bursts are assumed to be products of three-wave interaction processes of beam-excited Langmuir waves. Using a particle-in-cell code, we have performed simulations of the assumed emission region, a CME foreshock with two counterstreaming electron beams. Analysis of wavemodes within the simulation shows self-consistent excitation of beam driven modes, which yield interaction products at both fundamental and harmonic emission frequencies. Through variation of the beam strength, we have investigated the dependence of energy transfer into electrostatic and electromagnetic modes, confirming the quadratic dependence of electromagnetic emission on electron beam strength.

Second harmonic electromagnetic emission of a turbulent magnetized plasma driven by a powerful electron beam

The power of second harmonic electromagnetic emission is calculated for the case when strong plasma turbulence is excited by a powerful electron beam in a magnetized plasma. It is shown that the simple analytical model of strong plasma turbulence with the assumption of a constant pump power is able to explain experimentally observed bursts of electromagnetic radiation as a consequence of separate collapse events. It is also found that the electromagnetic emission power calculated for three-wave interaction processes occurring in the long-wavelength part of turbulent spectrum is in order-of-magnitude agreement with experimental results.

Quantum turbulence cascades in the Gross-Pitaevskii model

We present a numerical study of turbulence in Bose-Einstein condensates within the 3D Gross-Pitaevskii equation. We concentrate on the direct energy cascade in forced-dissipated systems. We show that behavior of the system is very sensitive to the properties of the model at the scales greater than the forcing scale, and we identify three different universal regimes: (1) a non-stationary regime with condensation and transition from a four-wave to a three-wave interaction process when the largest scales are not dissipated, (2) a steady weak wave turbulence regime when largest scales are dissipated with a friction-type dissipation, (3) a state with a scale-by-scale balance of the linear and the nonlinear timescales when the large-scale dissipation is a hypo-viscosity.

Simulation Study of Plasma Emission in Beam-Plasma Interactions

A two-dimensional electromagnetic particle-in-cell simulation of the beam-plasma interaction process is carried out to study the electromagnetic radiation at the plasma frequency and its second harmonic. In the simulation, a homogeneous plasma background with a periodic boundary condition is assumed. Electromagnetic radiation at the plasma frequency and its higher harmonics are widely believed to be responsible for solar type-II and type-III radio bursts. Traditional theory based upon weak turbulence of three-wave and nonlinear wave-particle interaction processes predicts radiation emission primarily at the fundamental and second harmonic of the plasma frequency. Electrostatic modes and electromagnetic radiation corresponding to this expectation at the fundamental and the second harmonics plasma frequencies are found. The radiation patterns of the fundamental and second harmonic electromagnetic modes are examined in detail.

Development of electrostatic turbulence from drift-interchange instabilities in a toroidal plasma

Electrostatic instabilities develop on TORPEX (TORoidal Plasma EXperiment) [A. Fasoli et al., Phys. of Plasmas, 13, 55902 (2006)] in the bad curvature region and propagate consistently with the drift wave dispersion relation. The wave number and frequency spectra are coherent at the location where the instabilities are generated, then broaden along the E×B convection. The phase coupling between spectral components at different frequencies, measured at different locations over the plasma cross section, indicates that the transition from a coherent to a turbulent spectrum is mainly due to three-wave interaction processes. Nonlinear interactions are measured between the linearly unstable mode and fluctuations with larger frequency, with transfer of energy away from the linearly unstable mode. The results are consistent with a nonlinearity induced by the convection of density fluctuations by the E×B fluctuating velocity.

Wave turbulence in incompressible Hall magnetohydrodynamics

We investigate the steepening of the magnetic fluctuation power law spectra observed in the inner solar wind for frequencies higher than 0.5 Hz. This high frequency part of the spectrum may be attributed to dispersive nonlinear processes. In that context, the long-time behavior of weakly interacting waves is examined in the framework of 3D incompressible Hall MHD turbulence. The Hall term added to the standard MHD equations makes the Alfv\'en waves dispersive and circularly polarized. We introduce the generalized Els\"asser variables and, using a complex helicity decomposition, we derive for three-wave interaction processes the general wave kinetic equations; they describe the nonlinear dynamics of Alfv\'en, whistler and ion cyclotron wave turbulence in the presence of a strong uniform magnetic field $B_0 \ep$. Hall MHD turbulence is characterized by anisotropies of different strength. We show that electron and standard MHD turbulence can be seen as two frequency limits of the present theory but the standard MHD limit is singular; additionally, we analyze in detail the ion MHD turbulence limit. Exact power law solutions of the master wave kinetic equations are given in the small and large scale limits for which we have, respectively, the total energy spectra $E(\kpn,\kpa) \sim \kpn^{-5/2} |\kpa|^{-1/2}$ and $E(\kpn,\kpa) \sim \kpn^{-2}$. An anisotropic phenomenology is developed to describe continuously the different scaling laws of the energy spectrum; one predicts $E(\kpn,\kpa) \sim \kpn^{-2} |\kpa|^{-1/2} (1+\kpn^2d_i^2)^{-1/4}$. Nonlocal interactions between Alfv\'en, whistler and ion cyclotron waves are investigated; a non trivial dynamics exists only when a discrepancy from the equipartition between the large scale kinetic and magnetic energies happens.

Three-wave interaction in dissipative systems: a new way towards secondary instabilities

We have identified a new mechanism of wave destabilization in nonlinear dissipative systems. This mechanism, which differs from the usual scheme of two complex Ginzburg–Landau equations, is associated with a three-wave interaction (TWI) process, in close analogy with nonlinear optics and plasma physics. We develop a paradigm from which we derive the wave number and threshold of the secondary instability. Numerically, we obtain a good agreement with the theoretical predictions. Moreover, we numerically investigate a model which describes a real experiment and exhibits a regime of parameter where this mechanism is involved.

Practical use of a Lie algebra structure in non-dissipative fluid and plasma models

A class of Hamiltonian models is considered that both includes many important examples from fluid and plasma theory and admits an elementary and simple abstract formulation. The formalism is illustrated by explicit expressions for both incompressible and compressible ideal magnetohydrodynamics, including a Coriolis force term and, in the incompressible case, allowing for a sharp ideally conducting boundary. The small-amplitude expansion is studied for a general background state, and the abstract setting gives much control of the usually messy algebra. One result is a new general and surprisingly simple symmetric expression for the coupling strength in the resonant three-wave interaction process. It may provide a convenient starting point for wave coupling calculations and seems suitable for the use in conjunction with computer algebra when various concrete models are considered.

Hamiltonian theory for waves and the resonant three-wave interaction process

New theorems in the Hamiltonian theory of waves are used to study nonlinear resonant three-wave interaction. As an example a model for low-frequency electrostatic waves in a inhomogeneous plasma is used.