Weakly Turbulent MHD Waves in Compressible Low-Beta Plasmas

In this Letter, weak turbulence theory is used to investigate interactions among Alfven waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of magnetohydrodynamics, and extra terms are then added to model collisionless damping. These equations are used to provide a quantitative description of a variety of nonlinear processes, including "parallel" and "perpendicular" energy cascade, energy transfer between wave types, "phase mixing," and the generation of back-scattered Alfven waves.