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

Abstract

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.

Turbulence and Microprocesses in Inhomogeneous Solar Wind Plasmas

“…Whereas the PDFs calculated using the probabilistic model mentioned above [164] are consistent with those provided by the numerical simulations based on the dynamical model presented in this review [10,73], additional results have been obtained in the latter case. Figure 22 shows typical non-normalized probability distribution functions P log 10 |E| 2 and P (|E|) obtained as a function of log 10 |E| 2 and |E|, respectively, during the time interval ∆T, in the case of a quasi-homogeneous plasma with ∆n 0.001.…”

“…The statistical study of the electric fields' amplitudes is an additional tool to investigate Langmuir wave turbulence and, in particular, to understand the origin and the nature of the waveforms' modulations. Such works were performed using experimental data or owing to numerical simulations, for conditions typical of the solar wind [73,154,155], the Earth electron foreshock [45,156] or the cusp regions [157]. For example, large scale simulations showed that the statistics of Langmuir wave fields can be substantially modified by the presence of inhomogeneities.…”

“…Recently, the probability distribution functions of Langmuir waves' electric fields excited by weak electron beams in inhomogeneous plasmas were calculated owing to numerical simulations based on a probabilistic model of beam-plasma interaction [164] as well as on a self-consistent dynamical model involving wave-particle and wave-wave interactions [10,73]. In the first case, a powerful method proposed by Pearson [163] was used in order to classify the field distributions according to their first four statistical moments, each class corresponding to well known distributions.…”

“…Therefore the authors performed a series of exhaustive studies on turbulent Langmuir waves generated by energetic electron beams in weakly magnetized solar wind plasmas with random density fluctuations [10,38,56,[64][65][66][67][68][69][70][71][72][73][74][75][76][77]. They proposed a new approach to study microphysical phenomena occurring in the solar wind and coronal plasmas and built theoretical and numerical tools describing the dynamics of wave turbulence and beams in such inhomogeneous plasmas.…”

On the Efficiency of the Linear-mode Conversion for Generation of Solar Type III Radio Bursts

“…It predicted that the distribution of the amplitudes of the Langmuir waves in type III source regions should correspond to log-normal distribution. While some observations (Robinson et al 1993;Píša et al 2015) show good agreement with this prediction, there are numerous reports of observations and simulations (Krasnoselskikh et al 2007;Vidojevic et al 2012;Reid & Kontar 2017;Voshchepynets et al 2017) that show deviations of the distribution of the amplitudes of the Langmuir waves from log-normal can be rather significant.…”