## 4. Current-carrying magnetic flux tubes in the photosphereThe formation of intensive axially symmetric flux tubes with
(), Supposing , , , where , , and are Alfvén, sound and free-fall velocities, respectively we obtain from Eqs. (2) and (3) the following expressions for the magnetic field components of a steady-state flux tube (Zaitsev 1996): where Let us suppose the following approximations for the plasma convection velocity field near a steady-state magnetic flux tube: where is the radius of a magnetic flux tube. For such a model of the convective flow in the photosphere, where , the solution for Eq. (5) can be expressed as (Zaitsev & Khodachenko 1997): where , and = . It follows from Eq. (6) that for magnetic field has a maximum on the axis of the tube and decreases with increasing . Assuming that at the tube boundary the magnetic field value appears to be much less than , we can estimate from Eq. (6) the radius of flux tube (Zaitsev & Khodachenko 1997): In particular, if on the tube boundary , then
for the height km upon the level
, where cm Keeping in mind that on the boundary of the tube, in the region , the magnetic field becomes rather small and consequently the photospheric parameters, and Eq. (5), give the spatial behavior of the magnetic field: where is the magnetic Reynolds number. Thus, we have very rapid power-law decrease of the magnetic field vs. distance for , because in the photosphere. Taking Eq. (7) into account we obtain the total longitudinal current in the magnetic flux tube driven by the photospheric convection (Zaitsev 1997): Under the physical conditions of the upper photosphere in height h = 500 km upon the level , for the plasma flow velocity m/s, and the magnetic field G, Eq. (10) yields for the longitudinal current value A. Thus, thin magnetic flux tubes with strong magnetic field and
longitudinal currents of about 10 © European Southern Observatory (ESO) 1998 Online publication: August 27, 1998 |