MHD versus kinetic effects in the solar coronal heating: a two stage mechanism

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.