Astron. Astrophys. 333, 27-30 (1998)

2. The mean-field electrodynamics

The evolution of the mean magnetic field is governed by the dynamo equation

where is the turbulent electromotive force, , and the mean velocity of the differentially rotating interstellar gas (Krause & Rädler 1980).

2.1. The turbulent EMF

As usual, we assume approximate scale separation and write

The -tensor takes the form

with diagonal terms

turbulent diamagnetism

and magnetic buoyancy

Notice that the EMF varies with r, and z. This is caused by the nonaxisymmetry and the stratification in density and turbulent velocity (cf. Sect. 3.2 and 3.3 below). We simulate the nonaxisymmetric galactic pattern with enhanced density and turbulent velocity within the spiral arms. The different quenching functions represent the influence of the magnetic field strength onto the turbulence effects. The field strength is defined as with the equipartition field

A more detailed description of the EMF and the corresponding quenching functions are given in Elstner et al. (1996) and Kitchatinov & Rüdiger (1993).

In our calculations we have neglected any feedback of the magnetic field itself onto the eddy diffusivity. The scalar field is then given as

2.2. Ambipolar diffusion

The ambipolar drift velocity is proportional to the Lorentz force,

The mass density of ions is and is the ion-neutral collision frequency. In the following we set

(Brandenburg & Zweibel 1995).

© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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