Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of Short Large Amplitude Magnetic Structures (SLAMS)

A framework is described for estimating Linear growth rates and spectral energy transfers in turbulent wave-fields using two-point measurements. This approach, which is based on Volterra series, is applied to dual satellite data gathered in the vicinity of the Earth's bow shock, where Short Large Amplitude Magnetic Structures (SLAMS) supposedly play a leading role. The analysis attests the dynamic evolution of the SLAMS and reveals an energy cascade toward high-frequency waves.Comment: 26 pages, 13 figure

Identifying higher-order interactions in wave time-series

Reliable design and reanalysis of coastal and offshore structures requires, amongst other things, characterisation of extreme crest elevation corresponding to long return periods, and of the evolution of a wave in space and time conditional on an extreme crest. Extreme crests typically correspond to focussed wave events enhanced by wave-wave interactions of different orders. Higher-order spectral analysis can be used to identify wave-wave interactions in time-series of water surface elevation. The bispectrum and its normalised form (the bicoherence) have been reported by numerous authors as a means to characterise three-wave interactions in laboratory, field and simulation experiments. The bispectrum corresponds to a frequency-domain representation of the third order cumulant of the time-series, and can be thought of as an extension of the power spectrum (itself the frequency-domain representation of the second order cumulant). The power spectrum and bispectrum can both be expressed in terms of the Fourier transforms of the original time-series. The Fast Fourier transform (FFT) therefore provides an efficient means of estimation. However, there are a number of important practical considerations to ensuring reasonable estimation. To detect four-wave interactions, we need to consider the trispectrum and its normalised form (the tricoherence). The trispectrum corresponds to a frequency-domain (Fourier) representation of the fourth-order cumulant of the time-series. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum, depending on which of the two interactions is of interest. We consider both definitions in this paper. Both definitions can be estimated using the FFT, but it’s estimation is considerably more challenging than estimation of the bispectrum. Again, there are important practicalities to bear in mind. In this work, we consider the key practical steps required to correctly estimate the trispectrum and tricoherence. We demonstrate the usefulness of the trispectrum and tricoherence for identifying wave-wave interactions in synthetic (based on combinations of sinusoids and on the HOS model) and measured wave time-series

Predicting ion cyclotron emission from neutral beam heated plasmas in Wendelstein7-X stellarator

Measurements of ion cyclotron emission (ICE) are planned for magnetically confined fusion (MCF) plasmas heated by neutral beam injection (NBI) in the Wendelstein 7-X stellarator (W-7X). Freshly injected NBI ions in the edge region, whose velocity-space distribution function approximates a delta-function, are potentially unstable against the magnetoacoustic cyclotron instability (MCI), which could drive a detectable ICE signal. Prediction of ICE from NBI protons in W-7X hydrogen plasmas is challenging, owing to the low ratio of the ions' perpendicular velocity to the local Alfvén speed, v⊥(NBI)/vA ≃ 0.14. We address this from first principles, using the particle-in-cell (PIC) kinetic code EPOCH. This selfconsistently solves the Lorentz force equation and Maxwell's equations for tens of millions of computational ions (both thermal majority and energetic NBI minority) and electrons, fully resolving gyromotion and hence capturing the cyclotron resonant phenomenology which gives rise to ICE. Our simulations predict an ICE signal which is predominantly electrostatic while incorporating a significant electromagnetic component. Its frequency power spectrum reflects novel MCI physics, reported here for the first time. The NBI ions relaxing under the MCI first drive broadband field energy at frequencies a little below the lower hybrid frequency ωLH, across the wavenumber range kωc/VA= 40 to 60, where ωc and VA denote ion cyclotron frequency and Alfvén velocity. Nonlinear coupling between these waves then excites spectrally structured ICE with narrow peaks, at much lower frequencies, typically the proton cyclotron frequency and its lower harmonics. The relative strength of these peaks depends on the specifics of the NBI ion velocity-space distribution and of the local plasma conditions, implying diagnostic potential for the predicted ICE signal from W7-X

Methods for characterising microphysical processes in plasmas

Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres

In Situ Detection of Strong Langmuir Turbulence Processes in Solar Type III Radio Bursts

The high time resolution observations obtained by the WAVES experiment of the STEREO spacecraft in solar type III radio bursts show that Langmuir waves often occur as intense localized wave packets. These wave packets are characterized by short durations of only a few ms and peak intensities, which well exceed the supersonic modulational instability (MI) thresholds. These timescales and peak intensities satisfy the criterion of the solitons collapsed to spatial scales of a few hundred Debye lengths. The spectra of these wave packets consist of primary spectral peaks corresponding to beam-resonant Langmuir waves, two or more sidebands corresponding to down-shifted and up-shifted daughter Langmuir waves, and low frequency enhancements below a few hundred Hz corresponding to daughter ion sound waves. The frequencies and wave numbers of these spectral components satisfy the resonance conditions of the modulational instability (MI). Moreover, the tricoherences, computed using trispectral analysis techniques show that these spectral components are coupled to each other with a high degree of coherency as expected of the MI type of four wave interactions. The high intensities, short scale lengths, sideband spectral structures and low frequency spectral enhancements and, high levels of tricoherences amongst the spectral components of these wave packets provide unambiguous evidence for the supersonic MI and related strong turbulence processes in type III radio bursts. The implication of these observations include: (1) the MI and related strong turbulence processes often occur in type III source regions, (2) the strong turbulence processes probably play very important roles in beam stabilization as well as conversion of Langmuir waves into escaping radiation at the fundamental and second harmonic of the electron plasma frequency, fpe, and (3) the Langmuir collapse probably follows the route of MI in type III radio bursts

On the use of tricoherent analysis to detect non-linear wave-wave interactions

International audienceZur Beschreibung nichtlinearer Effekte in dispersiven Medien kann man den Ansatz der Drei- und Vier-Wellen-Wechselwirkungen verwenden. Man benötigt eine Analyse der Spektren höherer Ordnung, um sich gegenseitig beeinflussende Wellen in Zufallssignalen zu identifizieren. Das Bikohärenzspektrum, d.h. das normierte Kumulantenspektrum dritter Ordnung, ist in zahlreichen Untersuchungen zur Analyse von Drei-Wellen-Wechselwirkungen in numerischen, labormäβigen und natürlichen Experimenten verwendet worden. Hier entwickeln wir das Trikohärenzspektrum zur Detektion von Vier-Wellen-Wechselwirkungen. Wir berechnen statistische Eigenschaften des Trispektrums und von Trikohärenzschätzungen sowie das Vertrauensintervall der letzteren. Wir legen Ergebnisse numerischer Schätzungen der Trikohärenz zu synthetischen Signalen vor.For the description of non-linear effects in dispersive media, the approach of three- and four-wave interactions may be used. Higher-order spectral analysis is required for identifying interacting waves in random signals. The bicoherence spectrum, which is the normalized cumulant spectrum of the third order, has been applied to numerous studies for analysing three-wave interactions in numerical, laboratory and natural experiments. Here, we develop the Incoherence spectrum to detect four-wave interactions, calculate statistical properties of the trispectrum and tricoherence estimators as well as the confidence interval for the latter, and present results of numerical estimations of the tricoherence using synthetic signals.Afin de décrire les effets non-linéaires dans un milieu dissipatif, il est possible d'utiliser l'approche par interaction de trois ou quatre ondes. L'analyse spectrale d'ordre supérieur est nécessaire pour identifier les ondes en interaction dans les signaux stochastiques. Le spectre de bicohérence, qui est le spectre cumulant normalisé du troisième ordre, a été utilisé dans de nombreuses études pour analyser l'interaction de trois ondes dans des expériences numériques, de laboratoire ou naturelles. Ici, nous développons le spectre de tricohérence pour détecter les interactions de quatre ondes, calculons les propriétés statistiques du trispectre et des estimateurs de tricohérence, de même que l'intervalle de confiance pour ce dernier, et présentons le résultat d'estimations numériques de la tricohérence utilisant des signaux synthétiques