Solar Physics (2006) 237: 143–152 DOI: 10.1007/s11207-006-0141-2 C  Springer 2006 ON THE PROPAGATION AND DISSIPATION OF ALFV ´ EN WAVESIN CORONAL HOLES B.N. DWIVEDI and A.K. SRIVASTAVA Department of Applied Physics, Institute of Technology, Banaras Hindu University, Varanasi 221005, India (e-mail: bholadwivedi@yahoo.com) (Received 30 January 2006; accepted 25 May 2006; Published online 24 July 2006) Abstract. We underline the importance of Alfv´ en wave dissipation in the magnetic funnels through the viscous and resistive plasma. Our results show that Alfv´ en waves are one of the primary energy sources in the innermost part of coronal holes where the solar wind outflow starts. 1. Introduction There exist a vast literature on the potential role of magnetohydrodynamic (MHD) waves in understanding the outstanding problems of coronal heating and the so- lar wind acceleration mechanisms since the pioneering work of Parker (1965). Measurement of increasing line width with altitude above the limb by Hassler et al. (1990) was interpreted as the signature of outward propagating undamped Alfv´ en waves. More recently there have been a number of off-limb studies from CDS and SUMER spectrometers on the SOHO spacecraft (e.g., Wilhelm, Dwivedi, and Teriaca, 2004; Wilhelm et al., 2005; and references cited therein). While broadening of line profile with altitude is attributed to the propagating undamped Alfv´ en waves, the narrowing of the line profile at higher altitude may serve as likely signature of Alfv´ en wave dissipation (Harrison, Hood, and Pike, 2002). Singh et al. (2003) have found height variations of line profiles in the visible light that depended on the formation temperatures of the lines. The microscopic properties of the coronal hole plasma, e.g., viscosity and resistivity, etc., are im- portant for the conversion of mechanical energy of Alfv´ en waves into thermal energy. In this paper, we consider the viscous and resistive dissipation of Alfv´ en waves in the inner part of polar coronal holes ( R < 1.35 R ⊙ ) and investigate their relative role on the spatial variation of damping length scale, group velocity, and mechan- ical energy flux density of Alfv´ en waves. In Section 2, we describe the Alfv´ en wave propagation and dissipation. Results and discussion are given in the last section.