Space Physics Statistics of electric fields' amplitudes in Langmuir turbulence: A numerical simulation study

International audience; A systematic study of the properties of Langmuir turbulence generated by electron beams via bump-on-tail instabilities in strongly nonhomogeneous plasmas is presented. A statistical analysis of the Langmuir waves' amplitudes using numerical simulations based on two theoretical models is performed: a dynamical one and a probabilistic one. The former describes the self-consistent dynamics of wave-particle and wave-wave interactions. The latter is a modified version of the quasi-linear theory. To analyze the simulation data provided by the probabilistic model, a Pearson technique is used to classify the calculated probability distribution functions (PDFs) of the logarithm of the waves' amplitudes. It is demonstrated that the core parts of the PDFs belong to the Pearson types I, IV, and VI distributions, while the high-amplitude parts of the PDFs follow power law or exponential decay. Analysis of the PDFs calculated using the numerical simulations based on the dynamical model leads to the following additional results. In the small-amplitude parts of the PDFs, a universal scaling parameter is found, with a value not depending on the average levels of the density fluctuations and of the Langmuir turbulence. Second, the PDFs are obtained in the presence of wave decay processes. When those are weak, the PDFs show at large fields' amplitudes an exponential asymptotic behavior; during time evolution, the corresponding scaling parameter decreases until a universal probability distribution is reached, indicating that the wave decay processes are sufficiently strong. Such exponential type of distribution is a specific signature of transition states in the Langmuir turbulence.