Some problems of mean field electrodynamics

The mathematical structure which describes the evolution of the ensemble average of an electromagnetic field in an electrically conducting fluid in turbulent motion is often called mean field electrodynamics; the theory has significant application to cosmic magnetism. Recent studies of the theory by Lerche have cast doubt on several earlier conclusions of Steenbeck, Krause, and Radler, and it is the object of this paper to resolve the major points of conflict. In particular, defects are demonstrated in arguments which led Lerche to assert that isotropic, statistically steady, mirrorsymmetric turbulence can regenerate magnetic field in a conducting fluid. Also, a new development of a theory by Krause and Steenbeck is presented which shows that stochastic variations in conductivity do not promote the growth of fields of large wavelength. Subject heading: hydromagnetics