  We analyze the initial, kinematic stage of magnetic field evolution in an
isotropic and homogeneous turbulent conducting fluid with a rough velocity
field, v(l) ~ l^alpha, alpha<1. We propose that in the limit of small magnetic
Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the
smaller the roughness exponent, alpha, the larger the magnetic Reynolds number
that is needed to excite magnetic fluctuations. This implies that numerical or
experimental investigations of magnetohydrodynamic turbulence with small
Prandtl numbers need to achieve extremely high resolution in order to describe
magnetic phenomena adequately.
