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

Context. 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. Aims. 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. Methods. 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 Alfvénic, linearly polarised, plane wave is launched. Results. 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 Alfvén waves with the transverse density inhomogeneity. 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 Alfvén waves and, second, dissipation of these parallel electric fields via kinetic effects. It is shown that a single Alfvén wave harmonic with frequency ν = 7 Hz and longitudinal wavelength λA = 0.63 Mm, for a putative Alfvén speed of 4328 km s , the generated parallel electric field could account for 10% of the necessary coronal heating requirement. It is also shown that the amplitude of the generated parallel electric field exceeds the Dreicer electric field by about four orders of magnitude, which implies realisation of the run-away regime with associated electron acceleration. Conclusions. We conjecture that wide spectrum (10 − 10 Hz) Alfvén 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.