In this paper, a numerical model for the propagation of the shear Alfven waves (SAWs) on open magnetic field lines using a hybrid kinetic approach is presented.

There is a two-dimensional hybrid model: an ion component of plasma is described by a standard set of the MHD equations, while electrons are taken into account via the Vlasov equation. To solve the Vlasov equation, a particle-in-cell method (PIC) is used, and for solving the MHD and the Maxwell equations, finite difference methods are utilized.

The problem is as follows. A region of an inhomogeneous magnetic field is defined in the Earth's polar area. At the initial time, the Alfven wave arrives in this region and causes a disturbance in electron distribution function velocities. The problem is to find an electron distribution function and fields as the wave propagates along the field.