On Statistics of Electric Field Amplitudes in the Langmuir Turbulence
Résumé
We present a systematic study of the properties of the Langmuir wave turbulence generated by bump-on-tail instability in strongly non-homogeneous plasma. This type of turbulence occurs in numerous processes involving electrons beams in space plasmas. We analyse the synthetic data obtained in the numerical simulation based on two different approaches: the Hamiltonian model, and so-called probabilistic model. The Hamiltonian model describes in the self-consistent manner the wave-particle and wave-wave interactions in inhomogeneous magnetized plasmas. The model enables us to study the general properties of the distributions of the amplitudes of the Langmuir waves driven by the high-velocity electron beams in the fluctuating plasma. We pay special attention to the study of statistics of Languir waves under conditions when the decay instability, involving ion-sound waves, is developed. The probabilistic model, being modified version of the standard quasi-linear theory requires much less computational resources. Due to this it enables us to performed a detailed analysis of the statistics of the amplitudes of the Langmuir waves in the plasma with density fluctuations. To analyze data obtained in both numerical models, a Pearson technique was used to classify the probability distribution functions (PDF) of the logarithm of wave intensity. It was shown that core parts the PDF's belong to Pearson types I,IV and VI, depending on the spatial profiles of the density fluctuations, rather than to the normal distribution. The study also showed that the high-amplitude parts of the distributions follow power-low or exponential decay, depending on the type of core distribution.