Anisotropic weak turbulence of Alfven waves in collisionless astrophysical plasmas

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.