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

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

Generation of nonlinear electric field bursts in the outer radiation belt through the parametric decay of whistler waves

International audienceHuge numbers of different nonlinear structures (double layers, electron holes, nonlinear whistlers, etc., referred to as Time Domain Structures, TDS) have been observed by the electric field experiment on the Van Allen Probes. Some of them are associated with whistler waves. Such TDS often emerge on the forward edges of the whistler wave packets and form chains. The parametric decay of a whistler wave into a whistler wave propagating in the opposite direction and an electron acoustic wave is studied experimentally as well as analytically, using Van Allen Probes data. The resulting electron acoustic wave is considered to be the source of electron scale TDS. The measured parameters of the three waves (two whistlers and the electron acoustic wave) are in good agreement with an assumption of their parametric interaction: í µí¼ 0 = í µí¼ 1 + í µí¼ 2 and ⃗ k 0 = ⃗ k 1 + ⃗ k 2. The bicoherence analysis shows the nonlinear nature of the observed electron-acoustic waves as well as the whistler wave and electron acoustic wave phase relation. The estimated decay instability growth rate shows that the process of three-wave interaction can develop in a characteristic time smaller than 1 s, thus, the process is rapid enough to explain the observations. This induced parametric interaction can be one of the mechanisms for quasiperiodic TDS generation in the outer Van Allen radiation belt