Evolution of magnetic field curvature in the Kulsrud-Anderson dynamo theory

We find that in the kinematic limit, the ensemble-averaged square of the curvature of magnetic field lines is exponentially amplified in time by the turbulent motions in a highly conductive plasma. At the same time, the ensemble-averaged curvature vector exponentially decays to zero. Thus, independently of the initial conditions,, the fluctuation field becomes very curved, and the curvature vector becomes highly isotropic.