ABSTRACT
Mean field electrodynamics is concerned with the application of the techniques of mean field or quasi-linear theory to the derivation of local, turbulent transport equations for macroscopic quantities (such as the average magnetic field 〈B〉) in MHD and other plasma models. The most well-known products of mean field electrodynamics are the α and
β coefficients for the evolution of 〈B〉 in 3D, i.e., ∂
∂t 〈B〉 = ∇ × α〈B〉 + (η + β)∇2〈B〉, (1)
and the turbulent resistivity ηT in 2D, i.e.,
∂
∂t 〈A〉(x, t) = ηT ∂
∂x2 〈A〉, (2)
where A is the magnetic potential. (In (1) and (2) we have considered the simplest case, in which the underlying turbulence is assumed to be homogeneous and isotropic, and for which α, β and ηT are constant.) Of course, α is the familiar “dynamo coefficient”, which aims to capture, in a local transport coefficient, the fundamental process of amplification of field by cyclonic turbulence. Here α is a pseudo-scalar and nearly always depends on the turbulence helicity; β and ηT typically depend on the turbulence energy, but may involve other quantities. In addition, α, β and ηT each involve a field-fluid correlation time.
