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

¹ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
e-mail: teimuraz.zaqarashvili@oeaw.ac.at; maxim.khodachenko@oeaw.ac.at
² Departament de Matemàtiques i Informàtica. Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
e-mail: marc.carbonell@uib.es
³ Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain
e-mail: joseluis.ballester@uib.es
⁴ Abastumani Astrophysical Observatory at Ilia State University, University St. 2, Tbilisi, Georgia

Received: 6 June 2012
Accepted: 17 July 2012

Abstract

Context. Alfvén wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cut-off wavenumber, i.e. the Alfvén 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.

Aims. The aim of this paper is to point out the reason for the appearance of a cut-off wavenumber in single-fluid MHD.

Methods. Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description. We solved the dispersion relation of linear Alfvén waves at each step and sought the approximation responsible of the cut-off wavenumber appearance.

Results. We have found that neglecting inertial terms significantly reduces the real part of the Alfvén 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 Alfvén frequency becomes zero.

Conclusions. The appearance of a cut-off wavenumber, when Alfvén 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.