Equivalence of resistive evolution and kinetic dynamo models for stochastic magnetic fields

Abstract

The kinetic dynamo model of Jacobson and Moses [Phys. Rev. A 29, 3335 (1984)] and the resistive evolution model of Miller [Phys. Fluids 31, 1133 (1988)] are compared. Fourier analyzing the x dependence in slab geometry, both models reduce to an Ohm’s law for Fourier components of the form jk=F(k)Ek/η, where jk and Ek are the Fourier components of j∥ and E∥, η is the parallel resistivity, and F(k) is some function of k. The field line distribution function in the resistive evolution model can be chosen to make both models exactly equivalent, and implies that the characteristic field line length over which j∥/B is constant is the electron mean-free path. The time scale for validity of both models is t>τ, where τ is the electron collision time. The stochastic current spreading implied by these models is in rough quantitative agreement with recent measurements.