Numerical Analysis of Magnetic Field Amplification by Turbulence

We apply a Fourier spectral numerical method to 3D incompressible MHDturbulence with a magnetic Prandtl number $Pr \geq 1$. We examine the processesby which an initially weak, large-scale seed magnetic field and an initiallyweak, small-scale, impulse-like seed magnetic field are amplified. We find thatin both cases the magnetic energy spectrum grows at all scales. The growthrates at different amplification stages are analyzed. For a large-scale seedmagnetic field, the magnetic energy density grows as $\sim t^2$ for the firstfew turbulence eddy turnover times, followed by a dynamic growth stage, wherenonlinear interactions between different scales of the turbulence contribute toan exponential growth rate that is largely determined by the turbulence eddyturnover time. For a seed magnetic field that is initially set up at a smallscale in the turbulence, during the kinematic development stage, the growthrate of magnetic energy is $\propto 1/\tau_{max}$, where $\tau_{max}$ is theeddy turnover time of the smallest eddies of the turbulence. The kinematicgrowth stage is followed by a dynamic growth stage, where nonlinearity playsimportant role. During such dynamic growth stage, the growth rate of totalmagnetic energy is determined by both the magnetic energy amplification withinthe turbulence inertial range and that within the turbulence dissipation range.Comment: 41 pages, 12 figures, to be published in ApJ (vol. 556