Equilibrium velocity distributions in parallel propagating low-frequency Alfvénic turbulence

The equilibrium velocity distributions in parallel propagating, circularly polarized low-frequency Alfvénic turbulence are presented. The equilibrium solutions of the monochromatic Alfvén waves are extended to those of incompressible Alfvénic turbulence with the broadband spectrum in low beta plasmas. It is shown that the "apparent temperature" due to the nonresonant ion heating is explained on the basis of the equilibrium velocity distribution. The anisotropic equilibrium velocity distribution corresponding to Alfvénic turbulence in the Chew-Goldberger-Low system is also demonstrated. It is suggested that the distribution can be the back ground structure in the asymmetric velocity distributions observed in the solar wind.