Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation

Nonlinear evolution of circularly polarized Alfv\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\'n waves propagating from the photosphere.