Nonlinear decay of foreshock Langmuir waves in the presence of plasma inhomogeneities: Theory and Cluster observations

Abstract

[1] The intense high-frequency electrostatic waves observed in the terrestrial foreshock often have a form of a superposition of two monochromatic waves close to the plasma frequency. We suggest an interpretation of these spectra as signatures of nonlinear decay of Langmuir waves to electron-sound and ion-sound secondary waves. This decay instability is known to have different properties in inhomogeneous plasma, namely the threshold amplitude of this instability is inversely proportional to the scale of the inhomogeneity. We show that the observed dependence of the wave amplitude on the modulation scale of the wave packets is consistent with this property and the theory of absolute decay instability in inhomogeneous plasma can be applied to explain the satellite observations. In this study we used electric field data from the Wide Band Data instrument on board Cluster satellites.

Vlasov simulation of amplitude-modulated Langmuir waves

“…Strongly modulated waveforms and wave packets of Langmuir waves were commonly observed by spacecrafts in the auroral ionosphere, 1-4 the solar wind, [5][6][7] the electron foreshock region, [8][9][10] and the magnetotail. 11 The amplitude-modulated Langmuir waves were also observed in self-consistent kinetic simulations of electron beam instabilities.…”

Vlasov simulation of Langmuir wave packets

“…The observations in the magnetosphere have shown that the amplitude of Langmuir wave packets sometimes exceeds several hundred mV/m. The observed frequency spectra also show apparent double peaks around the electron plasma frequency with a small low-frequency component Bale et al, 1996;Soucek et al, 2005), which indicates the Langmuir decay instability. On the other hand, The GEOTAIL spacecraft observation in the magnetotail has shown that the amplitude of Langmuir wave packets is several hundred µV/m, which is too small for the Langmuir decay instability.…”

“…Correspondence to: T. Umeda (umeda@stelab.nagoya-u.ac.jp) waves were also observed in various regions of the magnetosphere, such as in the auroral ionosphere (Ergun et al, 1991;Stasiewicz et al, 1996;Bonnell et al, 1997;Pottelette et al, 1999;Lizunov et al, 2001), in the solar wind (Gurnett et al, 1993;Bale et al, 1996;Kellogg et al, 1999b), in the electron foreshock region (Kellogg et al, , 1999aSoucek et al, 2005), and in the magnetotail (Kojima et al, 1997).…”

“…The first is the parametric decay of Langmuir waves into ion acoustic waves (e.g. Cairns and Robinson, 1992;Cairns et al, 1998;Pottelette et al, 1999;Matsukiyo et al, 2004;Soucek et al, 2005) or lower hybrid waves (e.g. Stasiewicz et al, 1996;Bonnell et al, 1997;Lizunov et al, 2001).…”

New Exact Solutions of the System of Equations for the Ion Sound and Langmuir Waves by ETEM

“…Musher et al have submitted weak Langmuir turbulence [11]. In addition, some authors have focused on Langmuir waves [12][13][14]. Dodin et al have tackled Langmuir wave evolution in nonstationary plasma [15].…”