  Using Particle-In-Cell simulations i.e. in the kinetic plasma description the
discovery of a new mechanism of parallel electric field generation was recently
reported. Here we show that the electric field generation parallel to the
uniform unperturbed magnetic field can be obtained in a much simpler framework
using the ideal magnetohydrodynamics (MHD) description. In ideal MHD the
electric field parallel to the uniform unperturbed magnetic field appears due
to fast magnetosonic waves which are generated by the interaction of weakly
non-linear Alfv\'en waves with the transverse density inhomogeneity. In the
context of the coronal heating problem a new {\it two stage mechanism} of
plasma heating is presented by putting emphasis, first, on the generation of
parallel electric fields within an {\it ideal MHD} description directly, rather
than focusing on the enhanced dissipation mechanisms of the Alfv\'en waves and,
second, dissipation of these parallel electric fields via {\it kinetic}
effects. It is shown that for a single Alfv\'en wave harmonic with frequency
$\nu = 7$ Hz, and longitudinal wavelength $\lambda_A = 0.63$ Mm for a putative
Alfv\'en speed of 4328 km s$^{-1}$, the generated parallel electric field could
account for 10% of the necessary coronal heating requirement. We conjecture
that wide spectrum (10$^{-4}-10^3$ Hz) Alfv\'en waves, based on the
observationally constrained spectrum, could provide the necessary coronal
heating requirement. By comparing MHD versus kinetic results we also show that
there is a clear indication of the {\it anomalous resistivity} which is 100s of
times greater than the classical Braginskii value.
