Beam‐plasma interaction in randomly inhomogeneous plasmas and statistical properties of small‐amplitude Langmuir waves in the solar wind and electron foreshock

Abstract

[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.

On nonstationarity and rippling of the quasiperpendicular zone of the Earth bow shock: Cluster observations

“…These larger peaks may correspond to turbulent changes in the direction of the interplanetary magnetic field or the intrinsic burstiness of the Langmuir waves predicted by Stochastic Growth Theory (e.g. Robinson, 1995;Cairns and Robinson, 1999;Krasnoselskikh et al, 2007, and references therein).…”

Statistics of auroral Langmuir waves

“…It has since been applied to similar beam-driven Langmuir waves in the foreshocks of Earth and other planets Robinson, 1997, 1999;Boshuizen et al, 2001;Sigsbee et al, 2004;Krasnoselskikh et al, 2007) and type II bursts (Knock et al, 2001), mirror mode and electromagnetic ion cyclotron waves in Earth's magnetosheath (Cairns and Grubits, 2001), and waves near the electron plasma frequency in Earth's inner magnetosphere and polar cap (Burinskaya et al, 2000;Cairns and Menietti, 2001). These regions are all much more weakly magnetized (f ce /f pe 0.1) than the auroral context considered in this paper (f pe f ce ).…”

Waveform and envelope field statistics for waves with stochastically driven amplitudes

“…For instance, applications of SGT to Earth's foreshock showed that SOC and nonlinear processes are unimportant for the distributions of wave fields, at least for the events studied, and that SGT is applicable to various localized regions in the foreshock boundary. 4,5,[18][19][20] Such applications further demonstrated that spatial averaging results in qualitative and quantitative changes in the field distributions, e.g., from lognormal distributions without spatial averaging to power-law distributions with spatial averaging. 19,21 SGT predicts that intrinsic spatiotemporal variations in the conditions of the plasma ͑e.g., density fluctuations͒ and/or driver of the waves ͑e.g., an electron beam͒ produce fluctuations in the wave gain G͑t͒ = ͐ −ϱ t dt␥͑t͒, where ␥͑t͒ is the wave growth rate at time t. If many fluctuations occur during some characteristic time then the waves grow randomly and follow lognormal statistics for the envelope field E e , where E e 2 ͑t͒ ϰ e G͑t͒ .…”