Temporal properties of magnetohydrodynamic turbulence and Implications for Energetic Particle Transport*

The temporal properties of compressible magneto-hydrodynamic (MHD) turbulence is a fundamental problem which has important implications for particle acceleration and transport in astrophysical plasmas. Here, by analyzing the spatio-emporal properties of compressible MHD turbulence, we derive a new spectral power density function verified by simulations. This new function reveals that the low frequency fluctuations are dominated by modes with small parallel wavenumbers with respect to the mean background magnetic field. Furthermore, for fluctuations with dynamically significant parallel wavenumbers, broadening around their eigenfrequencies is described by this function in close agreement with simulations. We use this formalism to present the scaling properties of individual MHD modes. The broadening around eigenfrequencies is a direct consequence of nonlinear processes and is different for the three fundamental MHD modes. Our results provide a new window to investigate the temporal properties of turbulence and will enable further studies on the interaction between compressible MHD turbulence and energetic plasmas.