A few authors (Barnes and Sturrock, 1972; Ma, 1977; Svestka, 1977) have calculated the quantitative relationship between the static force-free field connecting the magnetic field and the twisting processes. They pointed out that the potential magnetic field without the current may be twisted into the force-free field with the enhanced current produced by the plasma rotation. Li et al. (1982) and Li and Hu (1984) have stated that the processes should be unsteady, and especially that they should not be static. The magnetic Reynold number is usually much larger than 100 in stellar atmosphere (Li et al., 1982). We adopt the following MHD equations:
where the force - free factor α (t, r) depends on both, t and r. According to t h e kinematical momentum conservation, the following constraint is easily obtained:
where V = (u, v, w) is the velocity field in the cylindrical coordinates. When studying the evolution of the kinematical force - free field, the in fluence of a reasonable flow on the variations of the magnetic field should be taken into account. After some reasonable simplification we deduce the specific expression of the variation law of the toroidal magnetic energy
where J1 is the Bessel function of the first order. In the active region, magnetic energy including the term of a twisted effect f(t) is larger than that of the static force - free field.