  The evolution of Alfven turbulence due to three-wave interactions is
discussed using kinetic theory for a collisionless, thermal plasma. There are
three low-frequency modes, analogous to the three modes of compressible MHD.
When only Alfven waves are considered, the known anisotropy of turbulence in
incompressible MHD theory is reproduced. Inclusion of a fast mode wave leads to
separation of turbulence into two regimes: small wave numbers where three-wave
processes involving a fast mode is dominant, and large wave numbers where the
three Alfven wave process is dominant. Possible application of the anisotropic
Alfven turbulence to the interstellar medium and dissipation of magnetic energy
in magnetars is discussed.
