2. The mean-field electrodynamics
2.1. The turbulent EMF
where is the turbulent electromotive force, , and the mean velocity (Krause & Rädler 1980). We employ cylindrical polar coordinates and assume an axisymmetry, . The drift velocity is due to the effect of ambipolar diffusion and is proportional to the Lorentz force (cf. Section 2.4).
Basic for the theory is the knowledge of the material vectors and tensors in front of large-scale magnetic field formations. The velocities and are playing the role of large-scale mean flows while the -tensor represents eddy diffusivity. Via a magnetic feedback all of them are influenced (`quenched') by the induced magnetic field. The various terms are discussed separately below.
2.2. Turbulent diamagnetism and pumping
(Kitchatinov & Rüdiger 1992). The latter function starts with unity for weak fields and vanishes like for strong fields. It is
with the equipartition value Eq. (1).
It starts with for weak fields and vanishes like for strong fields.
(cf. Fig. 1).
In Rüdiger et al. (1994) first consequences of this -quenching are demonstrated. Only oscillating modes provide magnetic fields of order of the turbulence-equipartition fields. The equipartition field strength in galaxies is about 3-5 . These values are comparable with observations. Steady modes, however, in totally nonlinear models get unrealistically large magnetic fields.
with the standard value (cf. Parker 1979; Ruzmaikin et al. 1988). The true is unknown, it can only be found if temporal variations (e.g. sunspot decay) are observed. In the present paper the standard value is used, but we also discuss values one order higher and one order lower. The correlation time is put as 30 Myr (Fröhlich & Schultz 1996).
2.4. Ambipolar diffusion
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997