  Using direct simulations of hydromagnetic turbulence driven by random
polarized waves it is shown that dynamo action is possible over a wide range of
magnetic Prandtl numbers from 10^-3 to 1. Triply periodic boundary conditions
are being used. In the final saturated state the resulting magnetic field has a
large-scale component of Beltrami type. For the kinematic phase, growth rates
have been determined for magnetic Prandtl numbers between 0.01 and 1, but only
the case with the smallest magnetic Prandtl number shows large-scale magnetic
fields. It is less organized than in the nonlinear stage. For small magnetic
Prandtl numbers the growth rates are comparable to those calculated from an
alpha squared mean-field dynamo. In the linear regime the magnetic helicity
spectrum has a short inertial range compatible with a -5/3 power law, while in
the nonlinear regime it is the current helicity whose spectrum may be
compatible with such a law. In the saturated case, the spectral magnetic energy
in the inertial range is in slight excess over the spectral kinetic energy,
although for small magnetic Prandtl numbers the magnetic energy spectrum
reaches its resistive cut off wavenumber more quickly. The viscous energy
dissipation declines with the square root of the magnetic Prandtl number, which
implies that most of the energy is dissipated via Joule heat.
