International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 811-816
On the coronal heating mechanism by the resonant absorption of Alfven waves
Department of Mathematics and Computer Science, Adelphi University, Garden City 11530, NY, USA
Received 31 December 1992
Copyright © 1993 H. Y. Alkahby. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we will investigate the heating of the solar corona by the resonant
absorption of Alfven waves in a viscous and isothermal atmosphere permeated by a horizontal
magnetic field. It is shown that if the viscosity dominates the motion in a high (low)- plasma,
it creates an absorbing and reflecting layer and the heating process is acoustic (magnetoacoustic).
When the magnetic field dominates the oscillatory process it creates a non-absorbing reflecting
layer. Consequently, the heating process is magnetohydrodynamic. An equation for resonance is
derived. It shows that resonances may occur for many values of the frequency and of the
magnetic field if the wavelength is matched with the strength of the magnetic field. At the
resonance frequencies, magnetic and kinetic energies will increase to very large values which may
account for the heating process. When the motion is dominated by the combined effects of the
viscosity and the magnetic field, the nature of the reflecting layer and the magnitude of the
reflection coefficient depend on the relative strengths of the magnetic field and the viscosity.