[1] A numerical model for wave propagation in an unstable plasma with inhomogeneities is developed. This model describes the linear interaction of Langmuir wave packets with an electron beam and takes into account the angular diffusion of the wave vector due to wave scattering on small-amplitude density fluctuations, as well as suppression of the instability caused by the removal of the wave from the resonance with particles during crossing density perturbations of relatively large amplitude. Using this model, the evolution of the wave packets in inhomogeneous plasmas with an electron beam is studied. To analyze data obtained both in space experiments and numerical modeling, a Pearson technique was used to classify the spectral density distributions. It was shown that both experimental distributions obtained within the Earth's foreshock aboard the CLUSTER spacecraft and model distributions for the logarithm of wave intensity belong to Pearson type IV rather than normal. The main reason for deviations of empirical distributions from the normal one is that the effective number of regions where the waves grow is not very large and, as a consequence, the central limit theorem fails to be true under the typical conditions for the Earth's electron foreshock. For large amplitudes, it is suggested that power law tails can result from variations of wave amplitudes due to changes of group velocity in the inhomogeneous plasma, in particular due to reflection of waves from inhomogeneities.

Abstract. A new method for remote sensing of the quasiperpendicular part of the bow shock surface is presented. The method is based on analysis of high frequency electric field fluctuations corresponding to Langmuir, upshifted, and downshifted oscillations in the electron foreshock. Langmuir waves usually have maximum intensity at the upstream boundary of this region. All these waves are generated by energetic electrons accelerated by quasiperpendicular zone of the shock front. Nonstationary behavior of the shock, in particular due to rippling, should result in modulation of energetic electron fluxes, thereby giving rise to variations of Langmuir waves intensity. For upshifted and downshifted oscillations, the variations of both intensity and central frequency can be observed. For the present study, WHISPER measurements of electric field spectra obtained aboard Cluster spacecraft are used to choose 48 crossings of the electron foreshock boundary with dominating Langmuir waves and to perform for the first time a statistical analysis of nonstationary behavior of quasiperpendicular zone of the Earth's bow shock. Analysis of hidden periodicities in plasma wave energy reveals shock front nonstationarity in the frequency range 0.33 f Bi

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