Recently using Particle-In-Cell simulations i.e .
in the kinetic plasma description Tsiklauri et al .
and Génot et al .
reported on a discovery of a new mechanism of parallel electric field generation , which results in electron acceleration .
In this work we show that the parallel ( to the uniform unperturbed magnetic field ) electric field generation can be obtained in much simpler framework using ideal Magnetohydrodynamic ( MHD ) description , i.e .
without resorting to complicated wave particle interaction effects such as ion polarisation drift and resulting space charge separation which seems to be an ultimate cause of the electron acceleration .
In the ideal MHD the parallel ( to the uniform unperturbed magnetic field ) electric field appears due to fast magnetosonic waves which are generated by the interaction of weakly non-linear Alfvén waves with the transverse density inhomogeneity .
Further , in the context of the coronal heating problem a new two stage mechanism of the plasma heating is presented by putting emphasis , first , on the generation of parallel electric fields within 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 ( \nu = 7 Hz ) , ( which has longitudinal wavelength \lambda _ { A } = 0.63 Mm for putative Alfvén speed of 4328 km s ^ { -1 } ) the generated parallel electric field could account for the 10 % of the necessary coronal heating requirement .
We conjecture that wide spectrum ( 10 ^ { -4 } -10 ^ { 3 } Hz ) Alfvén waves , based on observationally constrained spectrum , could provide necessary coronal heating requirement .
It is also shown that the amplitude of generated parallel electric field exceeds the Dreicer electric field by about four orders of magnitude , which implies realisation of the run-away regime with the associated electron acceleration .