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 ∼ L0/2, where L0 is the energy injection scale, while the most energy containing scale is∼ L0/5. The peak scale of spectrum of projected, two-dimensional field is∼ L0. (2) During the stage of magnetic field amplification, the energy equipartition scale shows a power-law increase of ∼ t, while the integral and curvature scales show a linear increase. The equipartition, integral, and curvature scales saturate at ∼ L0, ∼ 0.3L0, and ∼ 0.15L0, 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, σRM , in terms of the integral scale and rms strength of the IGMF, and estimated that σRM would be ∼ 100 and ∼ a few rad m for clusters and filaments, respectively. Subject headings: intergalactic medium — magnetic fields — MHD — turbulence Corresponding author.