scholarly journals Amplitude Modulation And Nonlinear Self-Interactions of the Geodesic Acoustic Mode at the Edge of MAST

Plasma ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 168-178
Author(s):  
Bogdan Hnat ◽  
Nicholas Walkden ◽  
Keyword(s):  
Amplitude Modulation ◽  
Low Frequency ◽  
Radial Electric Field ◽  
Plasma Potential ◽  
Acoustic Mode ◽  
Wave Interactions ◽  
Frequency Space ◽  
Mode Decomposition ◽  
Nonlinear Character ◽  
Geodesic Acoustic Mode

We studied the amplitude modulation of the radial electric field constructed from the Langmuir probe plasma potential measurements at the edge of the mega-ampere spherical tokamak (MAST). The Empirical Mode Decomposition (EMD) technique was applied, which allowed us to extract fluctuations on temporal scales of plasma turbulence, the Geodesic Acoustic Mode (GAM), and those associated with the residual poloidal flows. This decomposition preserved the nonlinear character of the signal. Hilbert transform (HT) was then used to obtain the amplitude modulation envelope of fluctuations associated with turbulence and with the GAM. We found significant spectral coherence at frequencies between 1–5 kHz, in the turbulence and the GAM envelopes and for the signal representing the low frequency zonal flows (LFZFs). We present the evidence of local and nonlocal, in frequency space, three wave interactions leading to coupling between the GAM and the low frequency (LF) part of the spectrum.

scholarly journals Geodesic acoustic mode oscillation in the low frequency range

2006 ◽  
Vol 13 (6) ◽  
pp. 062504 ◽  
Author(s):  
T. Watari ◽  
Y. Hamada ◽  
T. Notake ◽  
N. Takeuchi ◽  
K. Itoh
Keyword(s):  
Low Frequency ◽  
Acoustic Mode ◽  
Frequency Range ◽  
Mode Oscillation ◽  
Geodesic Acoustic Mode

scholarly journals On nonlinear self-interaction of geodesic acoustic mode driven by energetic particles

2010 ◽  
Vol 77 (4) ◽  
pp. 457-467 ◽  
Author(s):  
G. Y. FU
Keyword(s):  
Electric Field ◽  
Plasma Density ◽  
Second Harmonic ◽  
Fluid Model ◽  
Density Perturbation ◽  
Radial Electric Field ◽  
Energetic Particles ◽  
Acoustic Mode ◽  
Second Order ◽  
Geodesic Acoustic Mode

AbstractIt is shown that nonlinear self-interaction of energetic particle-driven geodesic acoustic mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second-order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second-order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

scholarly journals Trapped particle precession and sub-bounce zonal flow dynamics in tokamaks

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
W. Sengupta ◽  
A. B. Hassam
Keyword(s):  
Angular Momentum ◽  
Electric Field ◽  
Radial Electric Field ◽  
Zonal Flow ◽  
Acoustic Mode ◽  
Apparent Paradox ◽  
Zonal Flows ◽  
Long Wavelength ◽  
Particle Flows ◽  
Geodesic Acoustic Mode

A drift-kinetic calculation in an axisymmetric tokamak, with super-diamagnetic flows, is presented to elucidate the relation between the radial electric field, $E_{r}$, zonal flows and the rapid precession of the trapped particle (TP) population. It has been shown earlier (Rosenbluth & Hinton, Phys. Rev. Lett., vol. 80(4), 1998, p. 724, hereafter RH) that an initial radial electric field results in geodesic acoustic mode oscillations which subsequently Landau damp, resulting in a much smaller final residual electric field, and accompanying parallel zonal flows. We observe an apparent paradox: the final angular momentum in the RH parallel zonal flow is much smaller than the angular momentum expected from the well-known rapid precession of the trapped particle population in the RH residual electric field. We reconcile this paradox by illuminating the presence of a population of reverse circulating particle flows that, dominantly, are equal and opposite to the rapid TP precession. Mathematically, the calculation is facilitated by transforming to an energy coordinate shifted from conventional by an amount proportional to $E_{r}$. We also discuss the well-known RH coefficient in the context of effective mass and show how the TP precession and the opposite circulating flows contribute to this mass. Finally, we show that in the long wavelength limit, the RH flows and RH coefficient arise as a natural consequence of conservation of toroidal angular momentum and the second adiabatic invariant.

scholarly journals Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

2005 ◽  
Vol 55 (3) ◽  
pp. 349-360 ◽  
Author(s):  
A. V. Melnikov ◽  
L. G. Eliseev ◽  
A. V. Gudozhnik ◽  
S. E. Lysenko ◽  
V. A. Mavrin ◽  
...  
Keyword(s):  
Ion Beam ◽  
Heavy Ion ◽  
Plasma Potential ◽  
Acoustic Mode ◽  
Potential Oscillations ◽  
Geodesic Acoustic Mode ◽  
Heavy Ion Beam

APPLICATION OF THE EMPIRICAL MODE DECOMPOSITION METHOD TO GROUND-ROLL NOISE ATTENUATION IN SEISMIC DATA

2013 ◽  
Vol 31 (4) ◽  
pp. 619 ◽  
Author(s):  
Luiz Eduardo Soares Ferreira ◽  
Milton José Porsani ◽  
Michelângelo G. Da Silva ◽  
Giovani Lopes Vasconcelos
Keyword(s):  
Empirical Mode Decomposition ◽  
Seismic Data ◽  
Low Frequency ◽  
High Amplitude ◽  
Seismic Line ◽  
Seismic Processing ◽  
Mode Decomposition ◽  
Ground Roll ◽  
Fortran 90 ◽  
Emd Method

ABSTRACT. Seismic processing aims to provide an adequate image of the subsurface geology. During seismic processing, the filtering of signals considered noise is of utmost importance. Among these signals is the surface rolling noise, better known as ground-roll. Ground-roll occurs mainly in land seismic data, masking reflections, and this roll has the following main features: high amplitude, low frequency and low speed. The attenuation of this noise is generally performed through so-called conventional methods using 1-D or 2-D frequency filters in the fk domain. This study uses the empirical mode decomposition (EMD) method for ground-roll attenuation. The EMD method was implemented in the programming language FORTRAN 90 and applied in the time and frequency domains. The application of this method to the processing of land seismic line 204-RL-247 in Tacutu Basin resulted in stacked seismic sections that were of similar or sometimes better quality compared with those obtained using the fk and high-pass filtering methods.Keywords: seismic processing, empirical mode decomposition, seismic data filtering, ground-roll. RESUMO. O processamento sísmico tem como principal objetivo fornecer uma imagem adequada da geologia da subsuperfície. Nas etapas do processamento sísmico a filtragem de sinais considerados como ruídos é de fundamental importância. Dentre esses ruídos encontramos o ruído de rolamento superficial, mais conhecido como ground-roll . O ground-roll ocorre principalmente em dados sísmicos terrestres, mascarando as reflexões e possui como principais características: alta amplitude, baixa frequência e baixa velocidade. A atenuação desse ruído é geralmente realizada através de métodos de filtragem ditos convencionais, que utilizam filtros de frequência 1D ou filtro 2D no domínio fk. Este trabalho utiliza o método de Decomposição em Modos Empíricos (DME) para a atenuação do ground-roll. O método DME foi implementado em linguagem de programação FORTRAN 90, e foi aplicado no domínio do tempo e da frequência. Sua aplicação no processamento da linha sísmica terrestre 204-RL-247 da Bacia do Tacutu gerou como resultados, seções sísmicas empilhadas de qualidade semelhante e por vezes melhor, quando comparadas as obtidas com os métodos de filtragem fk e passa-alta.Palavras-chave: processamento sísmico, decomposição em modos empíricos, filtragem dados sísmicos, atenuação do ground-roll.

scholarly journals Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation

2019 ◽  
Vol 29 (05) ◽  
pp. 1930012 ◽  
Author(s):  
Yue Yu ◽  
Qianqian Wang ◽  
Qinsheng Bi ◽  
C. W. Lim
Keyword(s):  
Amplitude Modulation ◽  
Large Amplitude ◽  
Low Frequency ◽  
Slow Variable ◽  
Critical Manifold ◽  
Singular Orbit ◽  
Modulation Control ◽  
Cycle Oscillation ◽  
Tuning Frequency ◽  
Complex Mechanical Systems

Motivated by the forced harmonic vibration of complex mechanical systems, we analyze the dynamics involving different waves in a double-well potential oscillator coupling amplitude modulation control of low frequency. The combination of amplitude modulation factor significantly enriches the dynamical behaviors on the formation of multiple-S-shaped manifold and multiple jumping phenomena that alternate between epochs of slow and fast motion. We can conduct bifurcation analysis to identify two harmonic vibrations. One is that the singular orbit makes multiple jumps to a fast trajectory segment from one attracting equilibrium to another as the expression of slow variable by using the DeMoivre formula. With the increase of tuning frequency, the system exhibits relaxation-type oscillations whose small amplitude oscillations are produced by nonlinear local cycles together with a distinct large amplitude cycle oscillation accounting for the Melnikov threshold values. The tuning frequency may not only affect the asymptotic expressions for the solution curves near fold singularities but also allow for the large amplitude orbit vibrations near fold-cycle singularities. Numerical analysis for computing critical manifolds and their intersections is used to detect the dynamical features in this paper.

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