3. The equilibrium magnetic field configuration
We now present some asymptotic expansions for galactic dynamo models with the nonlinearity (5). First of all, we recognize that, because of the large parameter in the right hand side of Eq. (5), we can take
Thus for and for The function is derived by Rogachevskii and Kleeorin (2000). Note that in a more simplified model of turbulence the function (see Field et al. 1999). We stress that the qualitative behaviour of the model does not depend on these uncertainties in estimates for the scaling functions and .
we obtain for fields of quadrupole symmetry (cf. Kvasz et al., 1992)
Note that Eq. (14) differs from Eq. (11), arising from kinematic theory. For the specific choice of helicity profile and negative dynamo number D, there is an explicit steady solution, if we assume (remember that also , i.e. super-equipartition), of the form
where we have restored the dimensional factor . (Note that for this approximate solution.) This solution is remarkably close to the results from the naive Ansatz or , or the model of Moss et al. (1999). For example, the pitch angle of the magnetic field lines is for and .
© European Southern Observatory (ESO) 2000
Online publication: September 5, 2000