Pump Wave Amplitude Research Articles

Towards quantifying the effect of pump wave amplitude on cracks in the Nonlinear Coda Wave Interferometry method

In Non-Destructive Testing and Evaluation (NDT&E), an ultrasonic method called Nonlinear Coda Wave Interferometry (NCWI) has recently been developed to detect cracks in heterogeneous materials such as concrete. The underlying principle of NCWI is that a pump wave is used to activate the crack breathing which interact with the source probe signal. The resulting signal is then measured at receiver probes. In this work, a static finite element model (FEM) is used to simulate the pump wave/crack interaction in order to quantifies the average effect of the pump waves on a crack. By considering both crack opening and closure phases during the dynamic pump wave excitation, this static model aims to determine the pump stress amplitude for a given relative crack length variation due to the dynamic pump wave excitation at different amplitudes. Numerical results show, after reaching certain stress amplitude, a linear relationship between the relative crack length variation and the equivalent static load when considering a partially closed crack at its tips. Then, numerical NCWI outputs, e.g., the relative velocity change θ and the decorrelation coefficient Kd, have been calculated using a spectral element model (SEM). These results agree with previously published experimental NCWI results derived for a slightly damaged 2D glass plate.

Cascading parametric decay coupling between whistler and ion acoustic waves: Darwin particle-in-cell simulations

We present the results of numerical studies of the whistler wave parametric decay instability in the system with the suppressed Landau damping of ion acoustic waves (IAWs) based on the self-consistent Darwin particle-in-cell (PIC) model. It has been demonstrated that a monochromatic whistler wave launched along the background magnetic field couples to a counter-propagating whistler mode and co-propagating ion acoustic mode. The coupling of the electromagnetic mode to the electrostatic mode is guided by a ponderomotive force that forms spatio-temporal beat patterns in the longitudinal electric field generated by the counter-propagating whistler and the pump whistler wave. The threshold amplitude for the instability is determined to be δBw/B0 = 0.028 and agrees with a prediction for the ion decay instability: δBw/B0 = 0.042 based on the linear kinetic damping rates, and δBw/B0 = 0.030 based on the simulation derived damping rates. Increasing the amplitude of the pump whistler wave, the secondary and tertiary decay thresholds are reached, and cascading parametric decay from the daughter whistler modes is observed. At the largest amplitude (δBw/B0 ∼ 0.1) the primary IAW evolves into a short-lived and highly nonlinear structure. The observed dependence of the IAW growth rate on the pump wave amplitude agrees with the expected trend; however, quantitatively, the growth rate of the IAW is larger than expected from theoretical predictions. We discuss the relevant space regimes where the instability could be observed and extensions to the parametric coupling of whistler waves with the electron acoustic wave (EAW).

Quantification of the effect of pump wave amplitude on crack breathing for the Nonlinear Coda Wave Interferometry

In civil engineering, an emerging ultrasonic approach based on Code Wave Interferometry (CWI), called Nonlinear Coda Wave Interferometry (NCWI) has been developed to detect microcracks in cementitious materials that cannot be detectedby conventional ultrasonic methods. NCWI uses a high amplitude low frequency (LF) nonlinear pump wave to generate a nonlinear clapping effect at microcracks that can be detected by a high frequency (HF) probe wave. The imaging of cracks inside heterougeneous materials using NCWI requires the inversion technique, which is constitued by model space and data space, in which conatains model parameters and data parameters respectively. In the frame of inversion with NCWI, the model parameter used is the scatetring cross section of a crack sigmaD, and the experimental parameter is the decorrelation coefficient Kd. Knowing that sigmaD depends on the pump wave amplitude. Therefore, in order to introduce NCWI in inversion, the relationship between the pump wave and sigmaD is needed, which is the goal of this study. The dynamic pump wave generates clapping effect at crack tips, the probe wave frequencies are higher than the pump waves’ by an order of magnitude, hence the effect of pump wave on the coda wave is rather averaged. Previous study showed that this clapping effect is equivalent to a single crack length change dL, dL can be related to an equivalent static stress sigma0 which produces the same dL in quasi-static regime, which is equivalent to the dynamic pump wave. Therefore, a relation can be established between sigma0 and sigmaD. This introduces NCWI into the inverison. Then, the theoretical estimation of Kd can be achieved by the simulation of NCWI using 2D Spectral Element Method (SEM2D), combining with the relationship between sigma0 and sigmaD, which can be used later on in the inversion for the crack imaging.

Fluid and kinetic nonlinearities of near-acoustic plasma waves

Large amplitude, near-acoustic plasma waves have a temperature-dependent harmonic content and nonlinear frequency shifts. On cold plasmas, experiments show that fluid nonlinearities dominate, and the observed harmonic content is well predicted by a recent fluid analysis. In contrast, the measured nonlinear frequency shift is smaller than this theory prediction, suggesting the presence of other nonlinear effects neglected in this analysis. When the plasma is heated, kinetic effects become important, and we observe an increase in both the harmonic content and nonlinear frequency shift. Quantitative experiments on the stability of these large amplitude, near-acoustic plasma waves strongly support the idea that trapped particles reduce the amplitude threshold for instability below fluid models. At low temperatures, the broad characteristics of the parametric instability are determined by the frequency detuning of the pump and daughter wave and the wave-wave coupling strength, surprisingly consistent with simple cold fluid, three-wave theories. However, at higher temperatures, the pump wave becomes unstable at half the threshold pump wave amplitude, with similar exponential growth rates as for a cold plasma.

Trapped Particle Effects in the Parametric Instability of Near-Acoustic Plasma Waves.

Quantitative experiments on the parametric decay instability of near-acoustic plasma waves provide strong evidence that trapped particles reduce the instability threshold below fluid models. At low temperatures, the broad characteristics of the parametric instability are determined by the frequency detuning of the pump and daughter wave, and the wave-wave coupling strength, surprisingly consistent with cold fluid, three-wave theories. However, at higher temperatures, trapped particle effects dominate, and the pump wave becomes unstable at half the threshold pump wave amplitude with similar exponential growth rates as for a cold plasma.

An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing

The observed nonclassical power-law dependence of the amplitude of the second harmonic wave on the amplitude of a harmonic pump wave is explained as a phenomenon associated with two types of nonlinearity in a structurally inhomogeneous medium. An approach to solving the inverse problem of determining the nonlinearity parameters and the exponent in the above-mentioned dependence is demonstrated. To describe the effects of strongly pronounced nonlinearity, equations containing a double nonlinearity and generalizing the Hopf and Burgers equations are proposed. The possibility of their exact linearization is demonstrated. The profiles, spectral composition, and average wave intensity in such doubly nonlinear media are calculated. The shape of the shock front is found, and its width is estimated. The wave energy losses that depend on both nonlinearity parameters—quadratic and modular—are calculated.

Self-phase modulation pre-compensation of narrowlinewidth pulsed fiber lasers

High peak power, single frequency nanosecond fiber lasers have aroused the intense interest in their applications such as nonlinear frequency generation, LIDAR, and remote sensing. However, self-phase modulation (SPM) will induce a temporally dependent phase shift φNL (L, t)=|Ap (0, t)|2γLeff, where Ap is the amplitude of pump wave, γ is the nonlinear parameter, and Leff is the effective fiber length. The nonlinear phase shift will broaden the spectral linewidth of pulsed laser, which degrades the coherence of the laser and influences the performance of the laser. In order to obtain laser pulses with narrower linewidth, we can phase-modulate the pulsed laser with a value of-φNL(L,t). Thus, the SPM induced the nonlinear phase shift can be eliminated, and the spectra of pulsed laser can remain during the amplification and transmission in the fiber. Stimulated Brillouin scattering (SBS) has very low threshold and should be taken into consideration in narrow linewidth fiber lasers. The SBS threshold, which is dependent on the linewidth of laser, will be changed at the same time when the SPM is pre-compensated for. Because the SPM pre-compensation will change the linewidth of the pulsed laser. According to three coupled amplitude equations, we numerically analyze the influence of SPM pre-compensation on SBS threshold and spectral characteristics. The stimulation results show that in a master oscillator power amplifier structured fiber laser system, when SPM is completely compensated for (φM(t)=φNL(L,t)), the spectrum of the output pulsed laser can be maintained as that of the laser seed, but the SBS threshold usually decreases. When the SPM is compensated for incompletely (φM(t) φNL(L,t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed, and the SBS threshold in this situation is lower than the SBS threshold obtained when φM(t)=φNL(L,t). When the SPM is overcompensated for (φM(t) > φNL(L, t)), the spectral linewidth of the output laser cannot be compressed to that of the laser seed either, but the the SBS threshold in this situation is higher than the SBS threshold when φM(t)=φNL(L,t). We also build an experimental setup to verify the feasibility of SPM compensation. In our experiment, the linewidth of the pulsed laser is reduced from 1.4 GHz to 120 MHz when SPM is compensated for by phase modulation. The SBS threshold of the system are measured before and after SPM pre-compensation, and correctness of theoretical simulation is experimentally verified. This analysis method can provide the design guidelines for narrow-linewidth pulsed fiber laser systems.

Numerical modeling of ultrasonic coda wave interferometry in a multiple scattering medium with a localized nonlinear defect

In this paper, the spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous or heterogeneous sample with localized damage. The influence of a strong pump wave on localized nonlinear damage is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. These modifications are quantified with coda wave interferometry through an overall wave velocity variation probed by a reverberated or multiple scattered coda wave. Results demonstrate that the NCWI observables are independent of the source/receiver positions. Also, relations between the EDZ parameters and method observables are established, e.g. the relative velocity variation is found to be proportional to the product of the change in elastic modulus and the EDZ area. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for a quantitative non-destructive evaluation. Furthermore, it is shown numerically that NCWI sensitivity and applicability are similar for the cases of reverberated waves in a cavity and multiply scattered waves in a heterogeneous medium.

Analytical consideration and computer simulation of DFWM

Degenerate four-wave mixing (DFWM) for co-propagating femtosecond laser pulses is considered in the axial-symmetric case for bulk medium with cubic nonlinear response, if pump-wave amplitudes are being equal. Computer simulation is based on the set of nonlinear Schrödinger equations describing this process. For the analytical consideration we use the frame-work of both plane wave approximation and long pulse duration approximation taking into account the phase matching. In opposite to widely used approach, based on the pump-waves non-depletion, the problem invariants are used for analytical solution developing. The solution demonstrates various DFWM modes existence and allows us to provide full analysis of the problem in dependence of its parameters. Analytical solution and derived pulse interaction modes can explain complicated regime of DFWM, which may appear at different intensities of interacting waves.

Observation of an Alfvén Wave Parametric Instability in a Laboratory Plasma

A shear Alfvén wave parametric instability is observed for the first time in the laboratory. When a single finite ω/Ω_{i} kinetic Alfvén wave (KAW) is launched in the Large Plasma Device above a threshold amplitude, three daughter modes are produced. These daughter modes have frequencies and parallel wave numbers that are consistent with copropagating KAW sidebands and a low frequency nonresonant mode. The observed process is parametric in nature, with the frequency of the daughter modes varying as a function of pump wave amplitude. The daughter modes are spatially localized on a gradient of the pump wave magnetic field amplitude in the plane perpendicular to the background field, suggesting that perpendicular nonlinear forces (and therefore k_{⊥} of the pump wave) play an important role in the instability process. Despite this, modulational instability theory with k_{⊥}=0 has several features in common with the observed nonresonant mode and Alfvén wave sidebands.

On the formation of structures in nonequilibrium media in the resonant three-wave interaction

A mechanism of formation of flat and spiral solitary structures in nonequilibrium media allowing the resonant three-wave interaction of eigenmodes is proposed. A bifurcations diagram on the 'pump wave amplitude - initial profile width' plane is plotted

Particle-in-cell simulation for parametric decays of a circularly polarized Alfvén wave in relativistic thermal electron-positron plasma

Parametric decays of a left-handed circularly polarized Alfvén wave propagating along a constant background magnetic field in a relativistic thermal electron-positron plasma are studied by means of a one dimensional relativistic particle-in-cell simulation. Relativistic effects are included in the Lorentz equation for the momentum of the particles and in their thermal motion, by considering a Maxwell-Jüttner velocity distribution function for the initial condition. In the linear stage of the simulation, we find many instabilities that match the predictions of relativistic fluid theory. In general, the growth rates of the instabilities increase as the pump wave amplitude is increased, and decrease with a raise in the plasma temperatures. We have confirmed that for very high temperatures the Alfvén branch is suppressed, consistent with analytical calculations.

REGULATION OF ION DRIFTS AND ANISOTROPIES BY PARAMETRICALLY UNSTABLE FINITE-AMPLITUDE ALFVÉN-CYCLOTRON WAVES IN THE FAST SOLAR WIND

We study the preferential heating and differential acceleration of minor ions by dissipation of ion-acoustic waves (IAWs) generated by parametric instabilities of a finite-amplitude monochromatic Alfv?n-cyclotron pump wave. We consider the associated kinetic effects of Landau damping and nonlinear pitch-angle scattering of protons and ? particles in the tenuous plasma of coronal holes and the fast solar wind. Various data collected by Wind spacecraft show signatures for a local transverse heating of the minor ions, presumably by Alfv?n-cyclotron wave dissipation, and an unexpected parallel heating by a so far unknown mechanism. Here, we present the results from a set of 1.5 dimensional hybrid simulations in search for a plausible explanation for the observed field-aligned kinetic features in the fast solar wind minor ions. We investigate the origin and regulation of ion relative drifts and temperature anisotropies in low plasma ?, fast solar wind conditions. Depending on their initial drifts, both ion species can heat up not only transversely through cyclotron resonance and non-resonant wave-particle interactions, but also strongly in the parallel direction by Landau damping of the daughter IAWs. We discuss the dependence of the relative ion drifts and temperature anisotropies on the plasma ? of the individual species and we describe the effect of the pump wave amplitude on the ion heating and acceleration.

Third harmonic stimulated Raman backscattering of laser in a magnetized plasma

This article studies the nonlinear Raman shifted third harmonic backscattering of an intense extraordinary laser wave through a homogenous transversely magnetized cold plasma. Due to the relativistic nonlinearity, the plasma dynamic is modified in the presence of transversely magnetic field, and this can generate the third harmonic scattered wave and an electrostatic upper hybrid wave via the Raman scattering process. Using the nonlinear wave equation, the mechanism of nonlinear third harmonic Raman scattering is discussed in detail to obtain the maximum growth rate of instability in the mildly relativistic regime. The growth rate decreases as the static magnetic field increases. It also increases with the pump wave amplitude.

Parametric decays in relativistic magnetized electron-positron plasmas with relativistic temperatures

The nonlinear evolution of a circularly polarized electromagnetic wave in an electron-positron plasma propagating along a constant background magnetic field is considered, by studying its parametric decays. Relativistic effects, of the particle motion in the wave field and of the plasma temperature, are included to obtain the dispersion relation of the decays. The exact dispersion relation of the pump wave has been previously calculated within the context of a relativistic fluid theory and presents two branches: an electromagnetic and an Alfvén one. We investigate the parametric decays for the pump wave in these two branches, including the anomalous dispersion zone of the Alfvén branch where the group velocity is negative. We solve the nonlinear dispersion relation for different pump wave amplitudes and plasma temperatures, finding various resonant and nonresonant wave couplings. We are able to identify these couplings and study their behavior as we modify the plasma parameters. Some of these couplings are suppressed for larger amplitudes or temperatures. We also find two kinds of modulational instabilities, one involving two sideband daughter waves and another involving a forward-propagating electroacoustic mode and a sideband daughter wave.

Stimulated Raman back-scattering of a laser in a magnetized plasma channel

A Gaussian laser beam, propagating as an eigenmode through a low density plasma channel in the presence of an axial magnetic field, undergoes stimulated Raman back scattering, producing an upper hybrid wave and a radially localized electromagnetic sideband wave. The channel may be self created by the laser due to ponderomotive force or by a pre-pulse. The radial width of sideband is ≈a and Langmuir wave of extent b≈(aλD)1/2<<a. The nonlocal effect arising, due to self generated magnetic field, modifies the electron response to these Eigen modes, reduces the region of nonlocal interaction and hence the growth rate. The growth rate decreases with the pump wave amplitude and it maximum for back scattering. A nonlocal theory of stimulated Raman back-scattering of a laser, propagating through a plasma channel in the presence of an axial magnetic field, is developed. The laser excites a forward propagating upper hybrid mode, that is strongly localized radially, and a backward propagating electromagnetic wave-sideband. The growth rate significantly decreases with the magnetic field.

The effect of dust charge fluctuations on lower-hybrid suppression of drift waves in a magnetized plasma cylinder

The nonlinear coupling between drift waves and a lower-hybrid pump wave is studied in a magnetized dusty plasma cylinder. The growth rate and mode frequencies were evaluated based on typical dusty plasma parameters. It is found that the unstable drift mode frequency increases and the growth rate decreases sharply with the relative density of negatively charged dust grains. In addition, the growth rate and unstable mode frequency depend on pump wave amplitudes.

Parametric decay instability during high harmonic fast wave heating experiments on the TST-2 spherical tokamak

A degradation of heating efficiency was observed during high harmonic fast wave (HHFW) heating of spherical tokamak plasmas when parametric decay instability (PDI) occurred. Suppression of PDI is necessary to make HHFW a reliable heating and current drive tool in high β plasmas. In order to understand PDI, measurements were made using a radially movable electrostatic probe (ion saturation current and floating potential), arrays of RF magnetic probes distributed both toroidally and poloidally, microwave reflectometry and fast optical diagnostics in TST-2. The frequency spectrum usually exhibits ion-cyclotron harmonic sidebands f0 ± nfci and low-frequency ion-cyclotron quasi-modes (ICQMs) nfci. PDI becomes stronger at lower densities, and much weaker when the plasma is far away from the antenna. The lower sideband power was found to increase quadratically with the local pump wave power. The lower sideband power relative to the local pump wave power was larger for reflectometer compared with either electrostatic or magnetic probes. The radial decay of the pump wave amplitude in the SOL was much faster for the ion saturation current than for the floating potential. These results are consistent with the HHFW pump wave decaying into the HHFW or ion Bernstein wave (IBW) sideband and the low-frequency (ICQM). Two additional peaks were discovered between the fundamental lower sideband and the pump wave in hydrogen plasmas. The frequency differences of these peaks from the pump wave increase with the magnetic field. These decay modes may involve molecular ions or partially ionized impurity ions.

Non-cascade frequency-mixing processes for elastic waves in unconsolidated granular materials

Due to disorder, contacts between beads in stressed granular assemblages are not equally loaded. There exists a distribution of contact static loads, containing weakly loaded contacts (the weak contacts) and strongly loaded contacts (the strong contacts involved in the so-called force chains). For an elastic periodic excitation with a given deformation amplitude, the weakest contacts are supposed to clap (periodically open and close) due to the action of the acoustic wave. When increasing the acoustic amplitude, more and more contacts are clapping, progressively producing a non classical spectral signature. Presented spectra have been observed in a laboratory scale experiment, where two frequencies were initially launched in the medium. Results are obtained for increasing pump wave amplitudes and different frequency pairs. These experimental results are in good agreement with a model derived from the Hertz theory of contacts with possibility of clapping.

Alfvén wave filamentation and particle acceleration in solar wind and magnetosphere

We present numerical simulations of Alfvén waves in steady state, leading to the formation of intense magnetic filaments when the nonlinearity arises due to the ponderomotive effects and Joule heating. When the plain Alfvén wave is perturbed by a transverse perturbation and the magnitude of the pump Alfvén wave changes, chaotic filamentary structures of magnetic field in kinetic Alfvén wave (KAW) filamentation and quasiperiodic in inertial Alfvén wave (IAW) filamentation have been observed. At higher KAW pump wave amplitude, the spectra approaches near the Kolmogorov k−5/3 scaling. The spectral index becomes k−3 scaling in IAW. Relevance of these studies in solar wind and magnetosphere for KAW and solar corona and auroral region for IAW has also been pointed out. Particle heating in these small‐scale filamentary structures has also been calculated by using velocity space diffusion coefficient in Fokker‐Planck equation.