  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.
