  Particle-In-Cell (kinetic) simulations of shear Alfv\'en wave interaction
with one dimensional, across the uniform magnetic field, density inhomogeneity
(phase mixing) in collisionless plasma were performed for the first time. As a
result a new electron acceleration mechanism is discovered. Progressive
distortion of Alfv\'en wave front, due to the differences in local Alfv\'en
speed, generates nearly parallel to the magnetic field electrostatic fields,
which accelerate electrons via Landau damping. Surprisingly, amplitude decay
law in the inhomogeneous regions, in the kinetic regime, is the same as in the
MHD approximation described by Heyvaerts and Priest (1983).
