Wavelet Bicoherence Research Articles

Time‐resolved statistical analysis of nonlinear electrostatic fluctuationsin the ionospheric E region

Low‐frequency electrostatic fluctuations detectedby the instruments on the Rocket and Scatter Experiment (ROSE) rockets inthe E region over northern Scandinavia are analyzed.It is demonstrated that the time‐resolved statistical properties of the fluctuationsdeviate significantly from those associated with a Gaussian process. The characteristicsof the fluctuations are analyzed with particular attention to non‐Gaussianeffects and phase‐coherent mode couplings of electrostatic fluctuations. Non‐Gaussianeffects are analyzed by means of the kernel estimator for probability densityfor short data segments. Short‐time phase‐coherent effects are analyzed andquantified by means of the squared wavelet bicoherence, which has desirablestatistical properties in the frequency regions of interest. The results arecompared with similar results from rocket data obtained over SøndreStrømfjord in Greenland. The results show a remarkable similarity,indicating that the observed phase coherence is a robust feature of the saturatedstage of the E region instabilities.

Multiscale phenomena in the near-Earth magnetosphere

Several studies on the scaling properties of the near-Earth magnetosphere and auroral phenomena are reviewed. These studies employ modern analysis techniques that include fractal, multifractal, wavelet, wavelet bicoherence, and sign-singularity analyses as well as cellular automaton simulations of sandpile and avalanches. The results provide strong evidence for the multiscale, cross-scale coupling, and reorganization nature of auroral and magnetospheric phenomena, suggesting the possibility that the magnetosphere is in a forced and/or self organized critical state. Signatures of inverse cascade are found in magnetic fluctuations in current disruption events, which may indicate large-scale substorm features such as substorm current wedge and plasmoid may be evolved from small-scale plasma turbulence structures. Insights gained from these studies help to discriminate the existing competing substorm models. The multiscale properties of magnetospheric substorms are consistent with substorm models with intrinsic multiscale processes and not with substorm models with only a macroscopic process.

Structures, wavelet and intermittency in tokamak edge turbulence

The wavelet bicoherence technique is used to examine floating potential fluctuations in ADITYA tokamak edge plasma, which have shown vortex-like coherent structures on statistical basis [Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 583]. On a single discharge basis, the data exhibit intermittent episodes of quadratic interaction in which low and high frequency components are coupled. The broadband nonlinear phase coupling is used as a diagnostic signature of localized coherent structure. It is observed that the wavelet bicoherence is high in the presence of sparse structures and small when the structures are closely packed. The turbulent edge plasma has regions of packed Gaussian structures and sparse non-Gaussian structures.

Nonlinear analysis of turbulence across the L to H transition

Nonlinear time series analysis and wavelet bicoherence are used to characterize the changes to microturbulence in the radial electric field shear layer across the L to H transition in DIII-D. Time series of fluctuating floating potential and ion saturation current from the reciprocating probe array have been analysed for skewness and kurtosis as indications of intermittency in the turbulence. Provided the time series are carefully selected for stationarity, the skewness S and kurtosis K are consistent with Gaussian probability distributions in both L- and H-modes. Wavelet bicoherence analysis reveals the presence of intermittency in the coupling due to sum frequencies above 400 kHz in both the L- and H-modes. The intermittency is most pronounced in the H-mode, with the intervals of strong coupling correlated with changes in local edge plasma conditions. These results appear consistent with predictions from self-organized criticality models.

Wavelet analysis of ADITYA edge turbulence: Evidence of non-linear interaction

The edge turbulence in the ADITYA tokamak [Phys. Rev. Lett. 69, 1375 (1992)] is examined using wavelet analysis techniques. The wavelet filters are used to separate low and high frequency components. The filtered plasma density and floating potential fluctuations show leptokurtic non-Gaussianity (kurtosis, K≳3) at high frequencies, whereas, the low frequency components are nearly Gaussian. The recently developed wavelet bicoherence technique [Phys. Plasmas 2, 3017 (1995)] is extended to the Mexican hat wavelet. When the data are examined using wavelet bicoherence technique, it is found that the turbulent density and potential signals exhibit episodes of quadratic interaction in which low and high frequency components are coupled.

Wavelet bicoherence analysis of strong plasma turbulence at the Earth’s quasiparallel bow shock

Nonlinear interactions in strong plasma turbulence have been investigated in the vicinity of the Earth’s quasiparallel bow shock by making use of magnetometer data from the AMPTE–UKS (Active Magnetospheric Particle Tracer Explorers–United Kingdom Subsatellite) spacecraft. Using a new and more robust estimator of the bicoherence, it is shown that the large-amplitude monolithic magnetic structures observed upstream the shock front interact with the whistler wave trains that accompany them. A unified picture emerges, in which the whistlers progressively grow from these soliton-like structures through nonlinear interaction, similarly to the dynamical evolution of step-like profiles in the Korteweg–de Vries equation.

Wavelet bicoherence: A new turbulence analysis tool

A recently introduced tool for the analysis of turbulence, wavelet bicoherence [van Milligen, Hidalgo, and Sánchez, Phys. Rev. Lett. 16, 395 (1995)], is investigated. It is capable of detecting phase coupling—nonlinear interactions of the lowest (quadratic) order—with time resolution. To demonstrate its potential, it is applied to numerical models of chaos and turbulence and to real measurements. It detected the coupling interaction between two coupled van der Pol oscillators. When applied to a model of drift wave turbulence relevant to plasma physics, it detected a highly localized coherent structure. Analyzing reflectometry measurements made in fusion plasmas, it detected temporal intermittency and a strong increase in nonlinear phase coupling coinciding with the L/H (low-to-high confinement mode) transition.