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simulations of the ism in a shearing box domain have shown that turbulence driven by sne leads to an amplification of the mean magnetic field . using the test - field method ( schrinner et  al . @xcite ) , we derived transport coefficients relating the mean electromotive force to the mean magnetic field ( gressel  @xcite ) . with these we were able to reproduce the time behaviour seen in the simulations . under conditions found in our own galaxy , and assuming a constant circular velocity , a rotation rate @xmath0 was required for the dynamo to work . in order to further define the turbulence properties as a function of the star formation rate , rotation and gas density , we analysed a comprehensive set of direct simulations . taking these as an input , we here compute global mean - field maps for a set of different model galaxies . measuring test - field coefficients for a wide set of direct simulations ( gressel et  al . @xcite , @xcite ) led to the following scaling relations for the relevant diagonal term in the @xmath1  tensor , @xmath2 for the ( downward ) turbulent pumping described by the antisymmetric part of the @xmath1  tensor @xmath3 for the turbulent diffusivity @xmath4 and for the mean vertical outflow velocity @xmath5 the relations were derived for sf rates , @xmath6 , varying from one tenth up to the galactic value @xmath7 , angular velocities between @xmath8 and @xmath9 and midplane densities from @xmath10 up to @xmath11 . from the simulations , we moreover found a vertical gradient of the turbulent velocity @xmath12 independent of the star formation rate , density and angular velocity . we approximate the vertical profiles for the @xmath1  tensor by a @xmath13 curve with a scale height of @xmath14 . the value of @xmath15 is chosen to be constant for @xmath16 and linearly growing with a slope of one third outside this range . for simplicity , we assume a constant scale height within our models . we also neglect the anisotropic part of the turbulent diffusivity , which seems to be of minor importance for the current models . the rotation curve is modelled with a brandt law @xmath17 further we modify the vertical wind above @xmath18 by adding a radial outward velocity of the same size as @xmath19 . the wind velocities reach values of 100 - 200 km / s at z=4kpc , which is an order of magnitude higher than in the models of moss et al .  @xcite . with these input parameters , we solve the induction equation @xmath20 in a cylindrical domain with @xmath21 , and of vertical extent @xmath22 . defining @xmath23 and @xmath24 , we obtain a dynamo number @xmath25 . the pitch angle , @xmath26 , can be estimated by @xmath27 , scaling as @xmath28 . these estimates show that stronger sf reduces the dynamo number and increases the pitch angle . it is known that the stationary quadrupole solution of the @xmath29  dynamo exists only in a finite range of the dynamo number . because the final strength of the regular field also depends on the saturation process , this estimate does , however , not provide a prediction for the final field strength in dependence of the star formation . nevertheless , this behaviour still opens the possibility for radially extended regular magnetic fields . this is because , in an exponential disc , sf decays much faster with radius than the angular velocity , and hence the dynamo number may be nearly constant over a large radial range . +        applying a kenicutt  schmidt - type law , @xmath30 , we can specify our galaxy model by a radial density profile , which we leave constant up to @xmath31 and then exponentially decay with a scale length of @xmath32 , as seen in fig . [ fig : models ] . for the nonlinear back - reaction , we use a classical , however anisotropic , @xmath1  quenching . while the usual quenching of only the diagonal terms in the @xmath1  tensor would lead to solutions with a small pitch angle , independently quenching the pumping term can also saturate the dynamo by the increasing field advection from the wind . in this case , the pitch angle of the kinematic mode can be preserved ( elstner et  al . the models rely on a crude approximation of the vertical profiles for the turbulent transport coefficients , which still leave some uncertainty in the absolute numbers given in table  1 . nevertheless , the general trend agrees well with the predictions form the local dynamo number analysis . the pitch angle , measured from the magnetic vectors ( see fig .  [ fig : polmap ] ) of the polarisation map at @xmath31 , increases slightly with the star formation rate as predicted by the ratio @xmath33 above . the growth times of the order of @xmath34 tend to increase with the star formation rate , but there are exceptions ( cf . a1 and a2 of table  1 ) . no large - scale magnetic field amplification was observed for @xmath35 in model b3 , and in the weakly differentialy rotating model a5 . yet , strong starbursts are usually not long - lasting events and therefore the dynamo may still operate on longer time scales . the final field strength is not strongly dependent on the sf rate , and only the toroidal field is influenced by the difference in turbulent diffusivity . the inverse dependence of the dynamo action on the sf activity is mainly due to an enhanced turbulent diffusion . this does not necessarily increase the turbulent velocity but may equally change the correlation time . in fact , the preference of magnetic arms _ between _ the optical arms may be based on this very property of ism turbulence ( cf . rohde et al . @xcite ) . * sf rate and rotation determine the dynamo  calling for adequate galaxy evolution models . * low star formation rates favour the dynamo , explaining coherent inter - arm fields . * strong sf may suppress large - scale dynamo action ( no vertical fields in the centre ) . * explaining the radio - fir relation will require a different type of amplification mechanism  at least for the small - scale field . elstner d. , gressel o. , rdiger g. , 2009 , iaus  259 , 467 gressel o. , elstner d. , ziegler u. , rdiger g. , 2008 , a&a  486 , l35 gressel o. , 2009 , phd thesis , university of potsdam ( astro - ph:1001.5187 ) gressel o. , elstner d. , rdiger g. , 2011 , iaus  274 , 348 moss d. , sokoloff d. , beck r. , krause m. , 2010 , a&a  512 , a61 rohde r. , elstner d. , beck r. , 1999 , a&a  350 , 423 schrinner m. , rdler k .- h . , schmitt d. et  al . , 2005 , an  326 , 245
magnetic field amplification by a fast dynamo is seen in local box simulations of sn - driven ism turbulence , where the self - consistent emergence of large - scale fields agrees very well with its mean - field description . 
 we accordingly derive scaling laws of the turbulent transport coefficients in dependence of the sn rate , density and rotation . 
 these provide the input for global simulations of regular magnetic fields in galaxies within a mean - field mhd framework . using a kennicutt - schmidt relation between the star formation ( sf ) rate and midplane density 
 , we can reduce the number of free parameters in our global models . 
 we consequently present dynamo models for different rotation curves and radial density distributions .