  We study convective motions taken from hydrodynamic simulations of rotating
proto--neutron stars (PNSs) with respect to their ability to excite a dynamo
instability which may be responsible for the giant neutron star magnetic
fields. Since it is impossible to simulate the magnetic field evolution
employing the actual magnetic Reynolds numbers ($\Rm$) resulting from the
hydrodynamic simulations, (smallest) critical $\Rm$s and the corresponding
field geometries are derived on the kinematic level by rescaling the velocity
amplitudes. It turns out that the actual values of $\Rm$ are by many orders of
magnitude larger than the critical values found. A dynamo might therefore start
to act vigorously very soon after the onset of convection. But as in general
dynamo growth rates are non--monotonous functions of $\Rm$ the later fate of
the magnetic field is uncertain. Hence, no reliable statements on the existence
and efficiency of PNS dynamos can be drawn without considering the interplay of
magnetic field and convection from the beginning. Likewise, in so far as
convection inside the PNS is regarded to be essential in re--launching the
supernova explosion, a revision of its role in this respect could turn out to
be necessary.
