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

Cut-off wavenumber of Alfven waves in partially ionized plasmas of the solar atmosphere