  In this work we used Particle-In-Cell simulations to study the interaction of
circularly polarised Alfv\'en waves with one dimensional plasma density
inhomogeneities transverse to the uniform magnetic field (phase mixing) in
collisionless plasmas. In our preliminary work we reported discovery of a new
electron acceleration mechanism, in which progressive distortion of the
Alfv\'en wave front, due to the differences in local Alfv\'en speed, generates
an oblique (nearly parallel to the magnetic field) electrostatic field. The
latter accelerates electrons through the Landau resonance. Here we report a
detailed study of this novel mechanism, including: (i) analysis of broadening
of the ion distribution function due to the presence of Alfv\'en waves and (ii)
the generation of compressive perturbations due to both weak non-linearity and
plasma density inhomogeneity. The amplitude decay law in the inhomogeneous
regions, in the kinetic regime, is demonstrated to be the same as in the MHD
approximation described by Heyvaerts and Priest (1983).
