A Kinematical Theory of Turbulent Hydromagnetic Fields.
Abstract
A kinematical theory is developed for the r.m.s. magnetic fields produced by the interaction of turbulent eddies, of scale a and velocity v, with a largescale weak magnetic field B0. The principal interest lies in the smallscale magnetic field generated by the observed photospheric granules in the observed largescale photospheric magnetic fields. The theory considers how a rope of magnetic flux is both lengthened and widened by the velocity gradients in statistically stationary, isotropic, homogeneous turbulence in which the velocity fields are given. Both the amplification and diffusion of the magnetic field are then computed from the proportions of the rope of flux, employing the usual statistical assumption that moments of order 2n can be expressed in terms of the product of n factors of second moments. The conclusion is that a weak field B0 can be amplified by a factor of the order of R1/4/ln R, where R is the magnetic Reynolds number. in the solar photospheric granules this amounts to amplification by a factor less than 10, so that the smallscale r m 5. fields resulting in quiet regions where B0 __ 1 gauss are far below the value for equipartition of energy with the velocity field.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 1963
 DOI:
 10.1086/147629
 Bibcode:
 1963ApJ...138..226P