Physics of Magnetic Flux Tubes by Margarita Ryutova

Author:Margarita Ryutova
Language: eng
Format: epub, pdf
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(11.32)

By slight violation of the equivalence (11.32) toward increasing dispersion, roughly for thicker flux tubes, solitons become flat, their width increases, and their velocity drops. Thus, if the penumbral filament is thick enough, the kink produced by the shear flow instability will not survive. Finally, when the nonlinear term in (11.3) can be neglected, i.e., the problem becomes linear, a kink generated by shear flow after few undulations will disappear as usual wave. This will also happen if the dispersion term exceeds the nonlinearity by one or two orders of magnitude.

To estimate the radius of the flux tube at which in otherwise suitable conditions solitons do not form, we use two examples of a long-lived type I MMFs shown in Fig. 11.15 (panels 4 and 5).

The observed and estimated parameters are shown in Table 11.1. The first five columns are directly observed parameters. The two next columns containing and are values of Alfvèn and phase velocities deduced from observations. The value is calculated with (11.1). We must add this table to the values of an angle and radii that at given physical conditions are not suitable for the formation of MMFs. These are: for MMF 1, , , and for MMF 2, , .

We adopt the following values: the plasma density outside the flux tube g cm, the ratio of mass densities, , and the flux tube inclination in the developed soliton, , so that .Table 11.1Measured and estimated parameters of MMFs

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