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

Abstract

We solve numerically ideal, 2.5D, MHD equations in Cartesian coordinates, with a plasma beta of 0.0001 starting from the equilibrium that mimics a footpoint of a large curvature radius solar coronal loop or a polar region plume. 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 two stage mechanism of plasma heating is presented by putting emphasis, first, on the generation of parallel electric fields within an 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 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. The exact amount of energy that could be deposited by such waves through our mechanism of parallel electric field generation can only be calculated once a more complete parametric study is done. Thus, the "theoretical spectrum" of the energy stored in parallel electric fields versus frequency needs to be obtained.