The equations governing the behavior of a wholly or partly ionized gas moving in the presence of a magnetic field are given. It is emphasized that the electric conductivity is independent of the magnetic field strength in many cases of actual interest. The stationary case of a magnetic field arising from the nonrigid rotation of a gaseous body is considered. Such a field is of the toroidal type. Fields of poloidal type may arise by the contraction of magnetized interstellar matter towards a star. The increase of strength of a magnetic field in turbulent conducting matter (stellar or interstellar) is considered. The conclusion is reached that the turbulence of every order of magnitude leads finally to a magnetic field, the energy density of which corresponds roughly to the energy density of the turbulence considered. If the magnetic field was weak in the beginning, this state was reached at first by the turbulence of smallest scale and smallest velocity, and then by the turbulence of higher orders; hence, the magnetic field strength must change secularly, as long as this process goes on. If our galaxy had only weak fields in its earlier stages, the present magnetic field should correspond to the turbulent velocity associated with distances of the order of ${10}^3$ light years (between ${10}^{-6\mathrm{}}$ and ${10}^{-5\mathrm{}}$ gauss), and these fields should be more or less homogeneous over distances of this order. If there were already fields in the beginning, the present fields might be somewhat stronger.

• Received 11 October 1950

DOI:https://doi.org/10.1103/PhysRev.82.863