In this paper, two sets of equation are derived from a set of fundamental MHD equations with a dynamo field. The first set of equations, which governs the evolution of the energies of the mean magnetic field and the mean plasma velocity with time, couples not only the mean motions with turbulent motion but also the mean motions with each other. It is pointed out that the reversed field pinch (RFP) plasma described by this set of equations can spontaneously relax to the Taylor state. The second set of equations, which governs the evolution of the helicity of the mean field and the mean helicity of the fluctuating field, depicts the helicity transfer between the mean and fluctuating field. It is shown that in the RFP plasma there exists a fluctuation-induced mean current consisting of energetic electrons, the generation of which is dominated by the dynamo field and completely determined by the dynamo field at the edge, and the energetic electron flow sustains the field-reversal configuration and reduces the anomaly in the loop voltage.
A Hall dynamo model for the reversed field pinch