Taking the effect of two-fluid motion of plasma in Alfven waves into accoun
t, a nonzero parallel electric held can rise within the wave itself under c
ollisionless conditions. This leads to a kinetic dissipation of Alfven wave
s by the wave-particle resonant interaction and electron heating along the
ambient magnetic held lines. Employing the drift kinetic equation, we inves
tigated this electron-heating mechanism under the cool ion approximation. T
he result shows that the damping rate and the heating rate obviously depend
on the strength distribution of the ambient magnetic held, and that they r
each their maximum values at B-0 = B-m and B-0 = (1 + 2 alpha)B-1/2(m), res
pectively, for the perturbed held of delta B proportional to B-0(alpha), wh
ere B-m is the ambient magnetic field strength when upsilon(A) = upsilon(Te
). Finally, we propose that this heating mechanism can be applied to explai
n the brightness distribution of solar soft X-ray coronal loops.