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Astron. Astrophys. 357, 1073-1085 (2000)

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6. Nonlinear damping of the phase-mixed AWs in corona

As in the Discussion, we take the length-scale of the field-aligned inhomogeneity in a coronal hole [FORMULA] km, the transverse inhomogeneity length-scale ranging as 1 km [FORMULA] km, and wave amplitudes ranging from 0.01 to 0.03 for [FORMULA].

For wave frequencies [FORMULA] s-1 (see Discussion), the nonuniformity restrictions for the decay into counterstreaming waves may be satisfied. Then, using the damping rate (57) in (32), we find that the pump wave amplitude decays with height as

[EQUATION]

where the distance of nonlinear damping

[EQUATION]

To compare this height with the field-aligned wavelength we rewrite [FORMULA] as

[EQUATION]

where the coefficient before [FORMULA] strongly depends on the perpendicular nonuniformity length-scale [FORMULA].

Let us apply the above results to phase-mixed Alfvén waves in a coronal hole. Taking [FORMULA] m, [FORMULA], and [FORMULA] m, we obtain a low damping height in the coronal holes, varying in the range from [FORMULA] with [FORMULA] km, up to [FORMULA] with [FORMULA] km. Note that the ion gyroradius is nevertheless very small compared to [FORMULA] at these heights.

The corresponding transverse wavelengths, [FORMULA] km with [FORMULA] km and [FORMULA] km with [FORMULA] km, are much longer than the dissipative length-scale, [FORMULA] m. This is exactly the point we made in the Introduction that the effect of FLR in Alfvén waves comes into play at length scales which are much longer than [FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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