Non-diffusive corrections to the long-scale behaviour of ensembles of turbulent magnetic lines: application of the functional method

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Abstract
The transverse spreading of magnetic field lines in a turbulent plasma is investigated analytically in order to obtain a statistical characterization at large spatial scales. We develop a functional-integral method that allows us to calculate in a systematic way statistical averages of physical quantities that depend on the fluctuating field. The known magnetic diffusion coefficient for the shear-free case is corrected with a term arising from the assumption of a finite transverse correlation length. For the case with magnetic shear the functional method provides the appropriate framework for a perturbative approach based on diagram series.