The influence of the Alfven wave an the electron distribution function is s
tudied by numerical simulations. A quasi-linear operator models the electro
n Landau damping of any plasma eigenmodes: kinetic Alfven, whistlers, and l
ower hybrid waves. Weak collisions are taken into account via 2D in the vel
ocity space nonlinear Fokker-Planck kinetic equation. It is shown that due
to the variation of phase velocity, as seen by the Alfven wave in the cours
e of propagation in the nonuniform magnetic held the noninductive current i
nduced by the Alfven wave and the dissipated wave power may be several time
s larger in comparison with the case when the phase velocity is constant. T
he results might be applied in coronal regions, magnetosphere, tokamaks, st
ellarators.