On apparent temperature in low-frequency Alfvénic turbulence

Low-frequency, parallel propagating Alfvénic turbulence in collisionless plasmas is theoretically studied. Alfvénic turbulence is derived as an equilibrium state (Beltrami field) in the magnetohydrodynamic equations with the pressure anisotropy and multi-species of ions. It is shown that the conservation of the total "apparent temperature" corresponds to the Bernoulli law. A simple model of the radially expanding solar wind including Alfvénic turbulence is also discussed. The conversion of the wave energy in the "apparent temperature" into the real temperature is facilitated with increasing radial distance.