International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 587-594
On resistive dissipation of Alfvén waves in an isothermal atmosphere
Department of Mathematics and Computer Science, Dillard University, New Orleans 70122, LA, USA
Received 6 August 1994
Copyright © 1996 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 examine the reflection and dissipation of Alfvén waves, resulting from a
uniform vertical magnetic field, in an inviscid, resistive and isothermal atmosphere. An equation for the
damping length distance that wave can travel at Alfvén speed is derived. This equation shows that
the damping length is proportional to the wave number and the density scale height and it is valid not
only for Alfvén waves but also for any wave that travels at Alfvén speed. Moreover, it is shown that the atmosphere may be divided into two distinct regions connected by an absorbing and reflecting transition region. In the lower region the solution can be represented as a linear combination of two, incident and reflected, propagating waves with the same wavelengths and the same dissipative factors. In the upper region the effect of the resistive diffusivity and Alfvén speed is large and the solution, which satisfies the prescribed boundary conditions, either decays with altitude or behaves as a constant. In the transition region the reflection, dissipation and absorption of the magnetic energy of the waves take place. The reflection coefficient, the dissipative factors, which are proportional to the damping length, are determined and the conclusions are discussed in connection with heating of the solar atmosphere.