Normal modes of magnetic flux tubes and dissipation

¹ Institute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan 45195, Iran
² Department of Physics, Zanjan University, Zanjan, Iran
³ Center for Theoretical Physics and Mathematics, AEOI, PO Box 11345-8486, Tehran, Iran e-mail: Nasiri@iasbs.ac.ir;Sobouti@iasbs.ac.ir

Corresponding author: K. Karami, Karami@iasbs.ac.ir

Received: 19 April 2002
Accepted: 25 June 2002

Abstract

Wave propagation in a zero-β magnetic flux tube with a discontinuous Alfvèn speed at its surface is considered. The problem is reduced to solving a wave equation for the projection of the magnetic perturbation along the axis of the cylinder. The mathematical formalism is identical with that for the propagation of electromagnetic waves in optical fibers with a varying index of refraction in the cross section of the fiber. The dispersion relation is solved in its full generality and three wave numbers are assigned to the normal modes of the cylinder. There is a lower cutoff for the longitudinal wave number along the cylinder axis and an upper cutoff for the radial wave number. Eigenfrequencies and eigenfields (i.e. the magnetic and velocity fields of modes) are calculated. Resistive and viscous dissipation rates have mathematically identical forms, differing only in their being inversely proportional to the Lundquist and Reynolds numbers, respectively. These rates as well as the energy densities are obtained for each mode and are commented on.