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Astron. Astrophys. 354, 334-348 (2000)

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6. Discussion and conclusions

Let us put the results obtained in this paper into typical solar corona conditions. A coronal hole plasma is strongly inhomogeneous due to the presence of, for example, plumes, so phase mixing will occur when waves generated by photospheric motions travel outwards from the Sun. For example, if we assume that the plasma density inside a coronal plume is a factor of 4 higher than the surrounding plasma, we find [FORMULA]. If we further assume a driver with a 1-minute period and assume the Alfvén speed in a coronal hole to be 1000 km/s, we find that [FORMULA] solar radii. The pressure scale height [FORMULA] is found to be 0.2 solar radii for [FORMULA]K. With these values, we expect the maximum of the ohmic heating to occur at 1.4 solar radii and the maximum of the viscous heating at 1.35 solar radii (Fig. 12). When we consider a driver with a 5-minute period, the initial wavelength will be longer, which will cause to maximum of the ohmic and viscous dissipation to be situated at larger heights. So we find that for T=[FORMULA] K, a 1-minute oscillation will deposit most heat within a few solar radii and could therefore be a candidate for heating the coronal holes, while e.g. a 5-minute oscillation might be a way to deposit heat into the solar wind.

From studying the effect of a diverging background magnetic field on phase mixing of Alfvén waves in an open field region we conclude that wavelengths shorten when the waves propagate outwards. Therefore, phase mixing is more efficient and sufficiently small lengthscales for dissipation to be important will now build up faster. The waves will be dissipated quicker when compared to the standard non-diverging case. Due to the combination of the shortening of the wavelenghts and the enhanced efficiency of phase mixing, the maxima of the current density [FORMULA] occur at lower heights but at the same time are lower than in the Cartesian case. We found that, unlike in a non-diverging atmosphere, the current density and the vorticity behave in a similar manner and that ohmic and viscous heating will have a similar importance in the heating process.

From our study of the combined effect of a gravitationally stratified density and a radially diverging background magnetic field on phase mixing of Alfvén waves we found that the efficiency of phase mixing depends strongly on the particular geometry of the configuration. Finally, depending on the value of the scale height the wave amplitudes can damp either slower or faster than in the uniform non-diverging model.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000