Statistical properties of beam-driven upper-hybrid wave turbulence in the solar wind

We studied the statistical properties of beam-driven upper-hybrid wave turbulence in the solar wind by focusing on the probability density functions (PDFs) of electric field amplitudes, |E|. We used, for the first time, high-resolution and long-term 2D particle-in-cell simulations of the interaction of an electron beam with a magnetized plasma to calculate and analyse the skewness (degree of anisotropy) and the kurtosis (degree of flatness) of the PDFs of |E| and log|E|² for various intensities of plasma magnetization (Ω = w_c/w_p) and average levels of random density fluctuations (δN). Using the Pearson classification, we show that the PDFs of log|E|² predominantly align with Type VI Pearson distributions, with a shift towards Type I at high plasma magnetizations. In contrast, the PDFs of |E| are Type I Pearson distributions regardless of the Ω and δN values. Comparisons between simulation results and observations by the Solar Orbiter's Time Domain Sampler instrument show a good agreement. This study also offers a promising method for understanding the dynamics of wave turbulence and indirectly estimating plasma magnetization.