## 4. DiscussionWe have here discovered a two-dimensional, self-similar solution for phase mixing in an inhomogeneous magnetic field. It depends on a parameter, , which can be written as where the Lundquist number, , Using this solution, we have verified that an exp() height-dependence does exist, as predicted by Heyvaerts & Priest 1983, over a height range given by Fig. 8 shows that the height of maximum dissipation depends on
the value of and therefore on the values of
Consider the following example. For and
(corresponding to a high speed solar wind
blowing from a coronal hole) we require to
place the maximum ohmic heating in the range .
With these values, the wave dissipates within a few wavelengths
Limits on can also be used to place limits
on the Lundquist number If we further assume that at worst and at
best (Woo 1996) then :
this implies that we can dissipate Alfvén waves at reasonable
heights in the corona over a wide range of possible Lundquist number,
given a particular inhomogeneity scale. If either the background
Alfvén speed or the period of the
phase-mixed Alfvén wave is reduced, It should be noted that Alfvén waves with periods about and wavelengths on the order of should be observable by the CDS (Coronal Diagnostic Spectrometer) instrument on board the recently launched SoHO (Solar and Heliospheric Observatory) platform and that studies are in place to look for Alfvén waves in coronal holes (Harrison and Hassler 1995). Future theoretical work will concentrate on similar phase-mixing equations for different background Alfvén speed structures. © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |