Statistical analysis of the relationship between Power spectral density of magnetic turbulence and ion velocity in magnetotail bursty bulk Flows

Based on the observation of the THEMIS satellites, we utilize the superposed epoch method to statistically analyze how the p (Power Spectral Density) of compressional and transverse components of the magnetic field is affected by the ion inflow velocity V⊥ which is the peak velocity of BBFs (Bursty Bulk Flows). The analysis demonstrated that a modified scaling relationship p=C0V⊥γflog10C1V⊥χ is more suitable to describe the relationship than p∝f-α. The constant values of C0, γ, C1 and χ vary over the considered frequency ranges, velocity intervals, and components of magnetic field. These illustrate that in the study of turbulence the characteristic spectral index is incomplete to describe the energy cascade process, and the velocity is a key parameter in the study of the magnetotail plasma sheet turbulence.