Astron. Astrophys. 324, 11-14 (1997)

1. Introduction

The coronal heating mechanism remains one of the major unsolved problems in solar physics. Many mechanisms have been proposed for heating both closed and open field regions. In the open field regions of coronal holes, wave heating mechanisms remain an attractive possibility and recently Hood, Ireland and Priest (1996) presented an analytical solution to the phase mixing equations discussed in Heyvaerts and Priest (1983). Phase mixing occurs when the local Alfvén speed varies with position. Alfvén waves of the same frequency on different fieldlines travel with different speeds and hence have different wavenumbers. As they propagate they become out phase with their neighbours. This is phase mixing in space.

For standing Alfvén waves in closed field regions (such as the one described by Fig. 1), the Alfvén wavenumber is fixed by the finite size of the region. The inhomogeneous background Alfvén velocity makes the wave frequency space dependent, i.e.

for wavenumber , where L is the loop length. In a non-dissipative plasma, linear Alfvén waves of wavenumber k have solution , which implies

that is, gradients in the x -direction increase with time, implying that the waves are phase mixed in time. The different frequency on each field line means that initially in phase wave motions move out of phase with respect to each other, causing large Alfvén wave field gradients to appear across the loop. The small lengthscales created allow dissipation to have a large effect. To this end, we examine phase mixing in a coronal loop to establish its viability as a plausible loop heating mechanism, given typical solar parameters.

Fig. 1. Model of phase mixing in a coronal loop.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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