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We solve numerically ideal, 2.5D, MHD equations in Cartesian coordinates,with a plasma beta of 0.0001 starting from the equilibrium that mimics afootpoint of a large curvature radius solar coronal loop or a polar regionplume. On top of such an equilibrium, a purely Alfv\'enic, linearly polarised,plane wave is launched. In the context of the coronal heating problem a new twostage mechanism of plasma heating is presented by putting emphasis, first, onthe generation of parallel electric fields within an ideal MHD descriptiondirectly, rather than focusing on the enhanced dissipation mechanisms of theAlfv\'en waves and, second, dissipation of these parallel electric fields via{\it kinetic} effects. It is shown that a single Alfv\'en wave harmonic withfrequency $\nu = 7$ Hz and longitudinal wavelength $\lambda_A = 0.63$ Mm, for aputative Alfv\'en speed of 4328 km s$^{-1}$, the generated parallel electricfield could account for 10% of the necessary coronal heating requirement. Weconjecture that wide spectrum (10$^{-4}-10^3$ Hz) Alfv\'en waves, based on theobservationally constrained spectrum, could provide the necessary coronalheating requirement. The exact amount of energy that could be deposited by suchwaves through our mechanism of parallel electric field generation can only becalculated once a more complete parametric study is done. Thus, the"theoretical spectrum" of the energy stored in parallel electric fields versusfrequency needs to be obtained.Comment: Astron. Astrophys. (accepted, in press) (2006) - FULL pape

A mechanism for parallel electric field generation in the MHD limit: possible implications for the coronal heating problem in the two stage mechanism