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 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 for a single Alfvén wave harmonic with frequency \nu = 7 Hz , and longitudinal wavelength \lambda _ { A } = 0.63 Mm for a putative Alfvén 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 ) Alfvén 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 anomalous resistivity which is 100s of times greater than the classical Braginskii value .