Three-wave Coupling Research Articles

Use of differential plasma rotation to prevent disruptive tearing mode onset from 3-wave coupling

Abstract Plasma differential rotation is found to be capable of preventing disruptive neoclassical tearing modes (NTMs) seeded by nonlinear three-wave coupling. As tearing modes degrade confinement and can lead to disruptions, stabilization strategies are crucial to the successful operation of future devices. In ITER-relevant scenarios on DIII-D, rotationally coupled m / n = 1/1 and 3/2 modes have been observed to drive 2/1 islands through three-wave coupling. The frequency of the driven 2/1 mode is set by matching conditions and the frequencies of the driving modes. When the driven mode frequency matches the local plasma rotation frequency, e.g. at low differential rotation, the driven 2/1 island can grow into a disruptive NTM. Using neutral beam torque as an actuator to scan the differential rotation, these experiments demonstrate that a sufficiently large frequency mismatch prevents destabilization of disruptive 2/1 NTMs by three-wave coupling. This work indicates that differential rotation can be used as an actuator to prevent NTMs seeded by three-wave coupling.

Anisotropic magnon frequency comb based on antiferromagnetic bimerons

The interaction between propagating magnons and topological spin textures is attracting a lot of recent attention from the magnonic community. It has been shown that the three-wave mixing between magnons and breathing skyrmion can induce the magnon frequency comb (MFC) with equidistant coherent peaks. However, a magnetic bimeron is a nontrivial spin texture and is regarded as the counterpart of the skyrmion in easy-plane magnets with Dzyaloshinskii–Moriya interaction, which allows anisotropic magnon propagations. This raises the question of whether the nonlinear interaction between magnons and bimerons can generate an MFC. If so, how does the direction of magnon propagation affect the characteristics of the MFC? In this Letter, we demonstrate that the three-wave mixing between propagating magnons and locally breathing bimerons can induce a terahertz MFC in easy-plane antiferromagnets. Micromagnetic simulations reveal that the three-wave coupling strength weakly depends on the driving frequency, but it strongly relies on the propagation direction of incident magnons. Our findings uncover the anisotropic nature of MFC in bimeron structures, which may have potential applications for ultrafast magnonic devices with spectroscopy, metrology, and sensing functionalities.

Revisit of electron temperature effect on stimulated Brillouin scattering in homogenous plasma

Stimulated Brillouin scattering (SBS) has complex dependence on the plasma electron temperature via the Landau damping, particle trapping, and consequent nonlinear frequency shift. It is found from our numerical simulation that the SBS reflectivity in its saturation stage tends to increase with the plasma electron temperature within a certain range, although the linear growth rate of SBS normally reduces with the increasing electron temperature. This is because the phase velocity of an ion acoustic wave (IAW) increases with the electron temperature, which tends to reduce the Landau damping of the IAWs and hence reduce ion trapping. In the nonlinear saturation stage, ion trapping will modify the ion distribution function and induce a negative frequency shift in the IAW. This nonlinear frequency shift will break the three-wave coupling, thereby causing saturation of the SBS. With further increase in the electron temperature, however, electron trapping will dominate over ion trapping, which induces a positive frequency shift in the IAW and can lead to the SBS saturation as well. As a result, the SBS reflectivity first increases and then decreases with increase in the electron temperature. At around the peak of the SBS reflectivity, the positive frequency shift of IAW induced by electron trapping roughly offsets the negative frequency shift induced by ion trapping.

Inversion of electron densities in plasma wakes of hypersonic targets

Focusing on the plasma wakes of hypersonic targets (PWHT), this work provides a method for the inversion of electron densities in the PWHT by integrating electromagnetic radiation theory and three-wave coupling theory (TWCT). Utilizing the Computational Fluid Dynamics (CFD) method, taking a blunt cone as an example, the spatial distribution characteristics of electron densities in the plasma wake are simulated and analyzed in detail. The Zakharov system of equations (ZSE) is applied to the PWHT for the discussion about the electromagnetic radiation generated by plasma parametric instability. Combining the wavenumber spectrum of electromagnetic radiation and the TWCT, an inverse method of the electron densities of plasma wakes is proposed and applied to a blunt cone model. The results indicate that the inversion error rate is effectively held below 1.37 %. Furthermore, reasons for errors are elucidated through the utilization of the wavenumber spectrum structure. The proposed method may contribute to the development of hypersonic wake diagnostic techniques, and offer new insights and directions for wind tunnel experiments, shock tube experiments, as well as research on hypersonic target detection.

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

The photon blockade in a three-wave mixing system coupled with a quantum dot

In this paper, the photon blockade effect in a three-wave mixing coupling system with a quantum dot has been studied. By using analytical calculation and numerical analysis, we find that both the conventional photon blockade and the unconventional photon blockade effects could be realized in this system in strong-coupling regime just by one driving. Besides, compared with Jaynes–Cummings model, this hybrid system shows other obvious advantages in realizing the photon blockade, like blockading photon of more different frequencies, stronger antibunching effect. All the results may provide useful theoretical references for the single-photon devices design by using quantum dot and three-wave mixing system in future experiments and applications.

A transient flow analysis method for high-rate mud pulse telemetry in rotary steerable system

With the development of ultra-deep offshore and onshore deep-water wells, there is a growing demand for high-speed data transmission. Mud pulse telemetry (MPT) is the most commercially mature wireless data transmission method. The time-domain parameter analysis of the down-hole mud pulse pressure signal is useful to study the optimization measures of the down-hole signal. Currently, the main approaches are experiment and computational fluid dynamics (CFD) numerical simulations, but both methods are time-consuming and costly, which is not conducive to multi-parameter studies. transient flow modelis widely used to analyze water hammers in pipelines, but its application to mud pulse telemetry (MPT) systems has been less studied. In this paper, based on the classical transient flow equation, the method of characteristics (MOC) is used to solve the governing equation, and the boundary conditions suitable for the MPT are proposed and verified with the experiment and CFD method. Based on the newly established transient flow mathematical model, the generation characteristics of the downhole pressure wave and the influence law of key parameters are studied. The results show that the essence of continuous wave is a three-wave coupling of pressure wave, density wave and flow wave. With the transmission of continuous wave, unsteady friction will be generated in the wave region of the wellbore, increasing the attenuation degree of the signal. The amplitude of continuous wave increases with the increase of density and displacement, independent of frequency and viscosity. However, as the frequency and viscosity increase, the continuous wave will decay faster. This paper provides the new transient flow method with fast computational time and a technical means for MPT studies under subsequent drilling conditions.

Nonlinear processes and laser damage induced by a temporally modulated nanosecond UV laser beam. Part I: stimulated Brillouin scattering

Phase modulation is currently applied on pump laser beams propagating in thick optical elements to avoid optical damage induced by Brillouin backscattering. The experimental measurements show that adding a 2 GHz amplitude modulation to such a phase-modulated laser beam can compromise this optical preservation by increasing the Brillouin backscattering signal. These results are confirmed and explained with a theoretical analysis, developed in the perturbative regime, and with the numerical results obtained by solving three-wave coupling equations. Particularly, we show that when the frequency of the amplitude modulation is a harmonic of the phase modulation frequency, the Brillouin gain value is increased and can exceed the one obtained without amplitude modulation.

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

Edge turbulence transport during ELM suppression with n = 4 resonant magnetic perturbation on EAST

The edge turbulence characteristics and the induced radial transport have been investigated in edge localized mode (ELM) suppression by using the 4 resonant magnetic perturbation coils on EAST, with 3.6 and the electron collisionality 0.5. During ELM suppression, the edge turbulence is enhanced dramatically, as measured by the reciprocating probe and the poloidal correlation reflectometry. In the near SOL, the low frequency turbulence (<30 kHz) has a large fluctuation level and propagates along the ion diamagnetic drift direction with a speed of 0.35 km s−1 in the plasma frame; an electromagnetic mode around 120 kHz with a small (∼0.15 cm−1) appears when the ELM is suppressed; weak broadband turbulence between 40–120 kHz propagates in the electron diamagnetic drift direction with a velocity of 3.4 km s−1 in the plasma frame. During the ELM suppression, the radial turbulent particle flux, calculated in both the time and frequency domains, is much higher (can be up to five times) than that in the inter-ELM phase. Furthermore, the low frequency turbulence (<30 kHz) dominates the cross-field particle transport. The 120 kHz electromagnetic mode also contributes to outward particle flux, which is relatively small. A set of CGYRO simulations are performed to illustrate the nature of the 120 kHz electromagnetic mode and the low frequency turbulence, suggesting that the former is the micro-tearing mode and the latter is the ion temperature gradient mode. The bispectral analysis suggests a strong three-wave coupling between the low frequency and high frequency turbulence (>250 kHz), which could be beneficial to form the observed turbulent transport. The estimated upstream cross-field particle flux is consistent with the total particle flux deposited on divertor targets, demonstrating that the enhanced radial turbulent particle transport is an important mechanism for particle exhaust in ELM suppression.

Spectral broadening scheme for suppressing SBS effects based on time-domain optimized chirp-like signals.

We propose a novel (to our knowledge) driving scheme to suppress the stimulated Brillouin scattering (SBS) effect in master oscillator power amplification (MOPA) systems based on an external high-order phase modulation. Since seed sources with the linear chirp can uniformly broaden the SBS gain spectrum with a high SBS threshold, a chirp-like signal was designed by applying further editing and processing to the piecewise parabolic signal. Compared with the traditional piecewise parabolic signal, the chirp-like signal has similar linear chirp characteristics and can reduce the driving power and sampling rate requirements, enabling more efficient spectral spreading. The SBS threshold model is constructed theoretically based on the three-wave coupling equation. The spectrum modulated by the chirp-like signal is compared with the flat-top and Gaussian spectra in terms of the SBS threshold and the bandwidth-distribution normalized threshold, and a considerable improvement is demonstrated. Meanwhile, the experimental validation is carried out in a watt-class amplifier based on the MOPA structure. At a 3 dB bandwidth of ∼10 GHz, the SBS threshold of the seed source modulated by the chirp-like signal is improved by 35% compared to the flat-top spectrum and 18% compared to the Gaussian spectrum, respectively, and the normalized threshold is also the highest among them. Our study shows that the SBS suppression effect is not only related to the power distribution of the spectrum but also can be improved by the time domain design, which provides a new idea for analyzing and improving the SBS threshold of narrow-linewidth fiber lasers.

Mechanism of near-forward scattering driven photon acceleration in the interaction between an intense laser and under-dense plasmas

The mechanism of photon acceleration driven by the near-forward scattering (NFS) in the interaction between an intense laser and under-dense plasmas is studied by particle-in-cell (PIC) simulation. This mechanism utilizes tunneling ionization effect to stimulate electron plasma waves when the intense laser pulse propagates in under-dense plasmas. The electron plasma density is inhomogeneous both in longitudinal and transverse direction. In the longitudinal direction, a steep ionized electron density front is generated by incident laser ionizing the helium gas. Around the ionization front, the incident laser interacts with electron plasma waves, thus generating the first kind of NFS waves. Compared with the frequency of laser, the frequency of NFS wave increases. This is the first characteristic peak in the frequency spectrum. In the transverse direction, the electron plasma waves have different phase velocities, which makes the incident laser pulse undergo NFS process and upshift its frequency. This is the second characteristic peak in the frequency spectrum. Owing to the fact that the electron density inhomogeneity is much larger than the electron density perturbation of electron plasma wave, the scattering model and dispersion relationships, which are based on perturbation theory like stimulated Raman scattering, are no longer applicable to this case. Our further study shows that the incident laser, electron density plasma waves and NFS waves still satisfy the energy conservation and momentum conservation that is, they still satisfy the three-wave coupling relationship of momentum and energy conservation under the condition of heterogeneous density, thus explaining the appearance of two characteristic peaks in the frequency spectrum and their growth in the wave-vector space. This study has significant reference to the spectrum evolution when the intense laser pulse propagates in under-dense plasma.

Equations describing the direct relation between laser phase and Stokes light for SBS pumped by phase-modulated laser in optical fibers

Phase modulation is one of the most important methods to increase the threshold of the stimulated Brillouin scattering (SBS) in optical fibers. The mainstream theoretical model used to predict the SBS threshold is the transient three-wave coupling model. However, it is a general model and does not establish a straight relation between the laser phase and the Stokes light. In this paper, undepleted pump approximation is applied to the transient three-wave coupling model. Equations describing the evolution of the Stokes light in both time domain and frequency domain are derived. They establish a direct relation between the laser phase and Stokes light. All terms in the equations have clear physical interpretations. The equations are validated numerically by comparing with the original coupling model as well. It is found that the results match well when the Stokes average reflectivity is not greater than 1% which is usually used to define the SBS threshold.

On the role of bandwidth in pump and seed light waves for stimulated Raman scattering in inhomogeneous plasmas

The effects of incoherence on the three-wave coupling process of backward stimulated Raman scattering (SRS) in inhomogeneous plasmas are investigated theoretically and numerically via a three-wave coupling model. The impact of the plasma wave nonlinearity is taken into account, namely, the effect of trapped electrons via a nonlinear frequency shift of the electron plasma wave. Incoherence in the coupling is introduced in the seed wave, and the laser pump wave via bandwidth associated with a Lorentzian power spectrum. It is found that temporal incoherence can suppress the instability as long as the gain associated with spatial amplification in an inhomogeneous plasma (“Rosenbluth gain”) is smaller than 2. Otherwise, kinetic effects may destabilize SRS and significantly increase the backscatter level. For the bandwidth effects of the pump laser, a statistical analysis has been performed to examine the real impact of bandwidth. Moreover, a semi-analytical expression of the growth rate in the nonlinear stage is given. By estimating the bandwidth effects, it is found that a broad bandwidth of the pump laser starts to mitigate the scattering provided that the laser beam coherence time τc is shorter than γ0−1, the inverse of the standard SRS growth rate γ0. However, to obtain effective mitigation, by maintaining SRS in an almost linear stage, it is found that the criterion γ0τc≤0.35 has to be fulfilled.

A Study on Second Harmonic Excitation in Electron Beam–Plasma Instability

The electron beam–plasma interaction is a fundamental nonlinear plasma process that is frequently taking place in space and laboratory plasmas. Such an interaction is found to generate electromagnetic waves observed in space plasmas. Using the two-dimensional electromagnetic particle in cell simulations, we investigated the second harmonic excitation in the electron beam–plasma instability. Results showed that, first, the Langmuir waves are excited in the system; then at longer time scales, following the excitation of ion acoustic waves, the second harmonic electromagnetic waves are excited. We found that in the case of background pair plasmas, where the masses are the same, there is no signature of waves in the second harmonic, which is a direct verification of the three-wave coupling mechanism for the generation of electromagnetic waves in the second harmonic.

Temporal-filtering dissipative soliton in an optical parametric oscillator

Abstract Dissipative solitons have been realized in mode-locked fiber lasers in the theoretical framework of the Ginzburg–Landau equation and have significantly improved the pulse energy and peak power levels of such lasers. It is interesting to explore whether dissipative solitons exist in optical parametric oscillators in the framework of three-wave coupling equations in order to substantially increase the performance of optical parametric oscillators. Here, we demonstrate a temporal-filtering dissipative soliton in a synchronously pumped optical parametric oscillator. The temporal-gain filtering of the pump pulse combined with strong cascading nonlinearity and dispersion in the optical parametric oscillator enables the generation of a broad spectrum with a nearly linear chirp; consequently, a significantly compressed pulse and high peak power can be realized after dechirping outside the cavity. Furthermore, we realized, for the first time, dissipative solitons in an optical system with a negative nonlinear phase shift and anomalous dispersion, extending the parameter region of dissipative solitons. The findings may open a new research block for dissipative solitons and provide new opportunities for mid-infrared ultrafast science.

Reducing reflectivity of stimulated Raman scattering by discretely changing phase of incident light in inertial fusion plasmas

A new method to reduce the stimulated Raman scattering (SRS) in inertial confinement fusion conditions is proposed by changing the incident light phase discretely. The proposal is first examined by three-wave coupling equations and then verified by Vlasov simulations. A remarkable decreasing in SRS reflectivity is observed when the period of phase changing is less than where is the growth rate of SRS. By contrast, some simulations with continuously changing phase of incident light are carried out to compare their influence on SRS. In addition, the proposal may suppress the stimulated Brillouin scattering.

Mitigating parametric instabilities in plasmas by sunlight-like lasers

Sunlight-like lasers that have a continuous broad frequency spectrum, random phase spectrum, and random polarization are formulated theoretically. With a sunlight-like laser beam consisting of a sequence of temporal speckles, the resonant three-wave coupling that underlies parametric instabilities in laser–plasma interactions can be greatly degraded owing to the limited duration of each speckle and the frequency shift between two adjacent speckles. The wave coupling can be further weakened by the random polarization of such beams. Numerical simulations demonstrate that the intensity threshold of stimulated Raman scattering in homogeneous plasmas can be doubled by using a sunlight-like laser beam with a relative bandwidth of ∼1% as compared with a monochromatic laser beam. Consequently, the hot-electron generation harmful to inertial confinement fusion can be effectively controlled by using sunlight-like laser drivers. Such drivers may be realized in the next generation of broadband lasers by combining two or more broadband beams with independent phase spectra or by applying polarization smoothing to a single broadband beam.

Neoclassical Tearing Mode Seeding by Nonlinear Three-Wave Interactions in Tokamaks.

We report the experimental observation of seed magnetic island formation by nonlinear three-wave coupling of magnetic island triplets. In this experiment, disruptive 2,1 islands are seeded by the coupling of 4,3 and 3,2 tearing modes to a central 1,1 sawtooth precursor. Three-wave interactions between these modes are conclusively identified by bispectral analysis, indicating fixed phase relationships in agreement with theory. This new observation of this seeding mechanism has important implications for future reactors that must operate in stable plasma equilibria, free of disruptive 2,1 islands.

Gyrokinetic investigation of the nonlinear interaction of Alfvén instabilities and energetic particle-driven geodesic acoustic modes

This paper presents a study of the interaction between Alfvén modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed. At low energetic particle concentration, the zonal structure (identified as an energetic particle-driven geodesic acoustic mode) is more unstable than the Alfvén mode. In the regime at high energetic particle concentration, the Alfvén mode is more unstable than the zonal structure. The interplay between the modes leads to a modification of their growth rates as well as to a modification of their saturation levels. The theoretical explanation of the mode interaction is given in terms of three-wave coupling of the energetic particle-driven geodesic acoustic mode and Alfvén mode, mediated by the curvature–pressure coupling term of the energetic particles.