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

Abstract : 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.