Higher-Order Statistics and Nonlinear Processes in Space Plasmas

Statistics of order 2 (variance, auto and cross-correlation functions, auto and cross-power spectra) and 3 (skewness, auto and cross-bicorrelation functions, auto and cross-bispectra) are used to analyze the wave-particle interaction in space plasmas. The signals considered here are medium scale electron density irregularities and ELF/ULF electrostatic turbulence. Nonlinearities are mainly observed in the ELF range. They are independently pointed out in time series associated with fluctuations in electronic density and in time series associated with the measurement of one electric field component. Peaks in cross-bicorrelation function and in mutual information clearly show that, in well delimited frequency bands, the wave-particle interactions are nonlinear above a certain level of fluctuations. The way the energy is transferred within the frequencies of density fluctuations is indicated by a bi-spectra analysis.