  Alfven wave dynamics in partially ionized plasmas of the solar atmosphere
shows that there is indeed a cut-off wavenumber, i.e. the Alfven waves with
wavenumbers higher than the cut-off value are evanescent. The cut-off
wavenumber appears in single-fluid magnetohydrodynamic (MHD) approximation but
it is absent in a multi-fluid approach. Up to now, an explanation for the
existence of the cut-off wavenumber is still missing. The aim of this paper is
to point out the reason for the appearance of a cut-off wavenumber in
single-fluid MHD. Beginning with three-fluid equations (with electrons, protons
and neutral hydrogen atoms), we performed consecutive approximations until we
obtained the usual single-fluid description is obtained. We solved the
dispersion relation of linear Alfven waves at each step and sought the
approximation responsible of the cut-off wavenumber appearance. We have found
that neglecting inertial terms significantly reduces the real part of the
Alfven frequency although it never becomes zero. Therefore, the cut-off
wavenumber does not exist at this stage. However, when the inertial terms
together with the Hall term in the induction equation are neglected, the real
part of the Alfven frequency becomes zero. The appearance of a cut-off
wavenumber, when Alfven waves in partially ionized regions of the solar
atmosphere are studied, is the result of neglecting inertial and Hall terms,
therefore it has no physical origin.
