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

Morphology of Langmuir wave active sites in the Earth's foreshock observed from the four points CLUSTER constellation : analysis of a case event at small separation.

International audienceHigh frequency fluctuating electric field upstream from the Earth bowshock, at frequencies near the local electron plasma frequency Fpe, but varying within a considerable range (~ 0.1 to 1.1 Fpe), have been observed in situ by several plasma wave instruments. Referred to as `Langmuir waves' when found near the plasma frequency, as `upshifted'or `downshifted' oscillations when found above or below Fpe, they are associated with the flux of electrons which move upstream from the bowshock. The Cluster constellation offers a unique opportunity to perform a spatio-temporal analysis of the active sites of such electrostatic emissions when at small (~ 100 km) average separation. We present a case event taken in this context, over a few minutes time interval. The presence of so called 30 s (period) ULF waves in DC magnetic field and plasma density indicates a position in the ion foreshock. The HF electrostatic fluctuations are measured in the 2 - 80 kHz band with a good time resolution: the instrument performs signal acquisitions in snapshots of 6.3 ms duration at a recurrence of 13.3 ms, transmitting to ground a survey of large band signal variations at resolution 13.3 ms, and, at 107 ms recurrence, the accumulation of frequency spectra (at 160 Hz resolution) derived on board for all the snapshots. The HF fluctuations, as observed from the accumulated spectra, can be sorted in several classes: (a) thermal noise above the plasma frequency, the position of which is precisely measured by the sounder at regular intervals,(b)Langmuir waves in the close vicinity of Fpe, sometimes associated with emissions at 2 Fpe, (c) downshifted waves, (c)broadband noise at the low frequency end of the Whisper range.In many instances, more than one class (excluding thermal noise, always present) are associated in the same accumulated spectrum. Although the emissions are quite sporadic in term of amplitude variations, the global characteristics, in term of frequency signatures, can persist over a few seconds, the changes being seen on all spacecraft at nearby time boundaries. We can thus define regions, or active sites, of a given class (simple or composite) of frequency signatures. We shall present and discuss an analysis of a) the size and velocity of given regions (from simple boundary time analysis), b) occurrence of a given site as compared to global plasma parameters, such as DC magnetic field configuration, solar wind velocity, or global features in the ion and electron populations, c) directivity properties (in the antenna spin plane) of the spectral signatures, compared to DC magnetic field and solar wind velocity orientation