Vlasov simulation of nite amplitude magnetohydrodynamic waves in the solar wind : Development of Vlasov-Hall-MHD code

Vlasov simulation is a method to solve time evolution of a plasma by directly time advancing the distribution function in the position-velocity phase space. Vlasov simulation is free from thermal (numerical) noise and thus is advantageous in analyzing ne details of nonlinear plasma phenomena. With this background in mind, we have developed a new Vlasov simulation code (1-d in the real space, 3-d in the velocity space), in order to study basic properties of nonlinear evolution of large amplitude magnetohydrodynamic (MHD) waves in the solar wind. In contrast to traditional Vlasov simulations in which electron waves are of major concern, our simulation code focuses on solving plasma behavior around the ion scales, assuming a massless electron uid. Since we mainly deal with low frequency MHD waves propagating quasi-parallel to the background magnetic eld, cyclotron coupling can be assumed to be weak for parameters typical to the solar wind. Thus, in our code, the Vlasov equation is solved only along the longitudinal direction, whereas the Hall-MHD equations are solved for the transverse directions. Propagation properties of Alfv en and ion acoustic waves in the simulation agree with analytically obtained dispersion relations. Some results on the parametric decay instability of Alfv en waves are also reported.