Characteristic Lengths of Magnetic Field in Magnetohydrodynamic
  Turbulence
  In the framework of turbulence dynamo, flow motions amplify a weak seed
magnetic field through the stretching of field lines. Although the
amplification process has been a topic of active research, less attention has
been paid to the length scales of magnetic field. In this paper, we described a
numerical study on characteristic lengths of magnetic field in
magnetohydrodynamic turbulence. We considered the case of very weak or zero
mean magnetic field, which is applicable to the turbulence in the intergalactic
space. Our findings are as follows. (1) At saturation, the peak of magnetic
field spectrum occurs at $\sim L_0/2$, where $L_0$ is the energy injection
scale, while the most energy containing scale is $\sim L_0/5$. The peak scale
of spectrum of projected, two-dimensional field is $\sim L_0$. (2) During the
stage of magnetic field amplification, the energy equipartition scale shows a
power-law increase of $\sim t^{1.5}$, while the integral and curvature scales
show a linear increase. The equipartition, integral, and curvature scales
saturate at $\sim L_0$, $\sim 0.3L_0$, and $\sim 0.15L_0$, respectively. (3)
The coherence length of magnetic field defined in the Faraday rotation measure
(RM) due to the intergalactic magnetic field (IGMF) is related to the integral
scale. We presented a formula that expresses the standard deviation of RM,
$\sigma_{RM}$, in terms of the integral scale and rms strength of the IGMF, and
estimated that $\sigma_{RM}$ would be $\sim 100$ and $\sim$ a few rad m$^{-2}$
for clusters and filaments, respectively.
