7 research outputs found
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 BikohĂ€renzspektrum, d.h. das normierte Kumulantenspektrum dritter Ordnung, ist in zahlreichen Untersuchungen zur Analyse von Drei-Wellen-Wechselwirkungen in numerischen, labormĂ€ÎČigen und natĂŒrlichen Experimenten verwendet worden. Hier entwickeln wir das TrikohĂ€renzspektrum zur Detektion von Vier-Wellen-Wechselwirkungen. Wir berechnen statistische Eigenschaften des Trispektrums und von TrikohĂ€renzschĂ€tzungen sowie das Vertrauensintervall der letzteren. Wir legen Ergebnisse numerischer SchĂ€tzungen der TrikohĂ€renz 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 dĂ©crire les effets non-linĂ©aires dans un milieu dissipatif, il est possible d'utiliser l'approche par interaction de trois ou quatre ondes. L'analyse spectrale d'ordre supĂ©rieur est nĂ©cessaire pour identifier les ondes en interaction dans les signaux stochastiques. Le spectre de bicohĂ©rence, qui est le spectre cumulant normalisĂ© du troisiĂšme ordre, a Ă©tĂ© utilisĂ© dans de nombreuses Ă©tudes pour analyser l'interaction de trois ondes dans des expĂ©riences numĂ©riques, de laboratoire ou naturelles. Ici, nous dĂ©veloppons le spectre de tricohĂ©rence pour dĂ©tecter les interactions de quatre ondes, calculons les propriĂ©tĂ©s statistiques du trispectre et des estimateurs de tricohĂ©rence, de mĂȘme que l'intervalle de confiance pour ce dernier, et prĂ©sentons le rĂ©sultat d'estimations numĂ©riques de la tricohĂ©rence utilisant des signaux synthĂ©tiques
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: à ”ĂÂŒ 0 = à ”ĂÂŒ 1 + à ”ĂÂŒ 2 and â k 0 = â k 1 + â 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