  We investigate magnetic field amplification in a turbulent velocity field
with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan
model. We present the numerical solution of the model for the practically
important case of Kolmogorov distribution of velocity fluctuations, with a
large magnetic Reynolds number. We find that in contrast to the nonhelical case
where growing magnetic fields are described by a few bound eigenmodes
concentrated inside the inertial interval of the velocity field, in the helical
case the number of bound eigenmodes considerably increases; moreover, new
unbound eigenmodes appear. Both bound and unbound eigenmodes contribute to the
large-scale magnetic field. This indicates a limited applicability of the
conventional alpha model of a large-scale dynamo action, which captures only
unbound modes.

Astrophysics;Fluid Dynamics;Plasma Physics