Abstract Previous analytical and numerical investigations of the stochastic properties of field lines in magnetic turbulence have been based on determining the running field-line diffusion coefficient. The latter transport parameter is directly related to the second moment of the field-line distribution function. For the normal diffusive case, this distribution function should be a Gaussian where the width increases linearly with distance. The corresponding transport equation is a usual heat transport or diffusion equation. However, such an equation is no longer valid for nondiffusive cases. In this paper, we systematically develop a theory for obtaining a nondiffusive transport equation. The derived equation has the same structure as a generalized master equation. In the latter equation, we employ a so-called rapid decorrelation approximation to achieve a strong simplification. Its solution is a Gaussian regardless of whether the transport is subdiffusive, normal diffusive, or superdiffusive. For slab turbulence, where the theory of field line random walk is exact, we determine the running diffusion coefficient and the mean squared displacement for a general spectrum in the energy range. The same quantities are then computed by employing numerical simulations. It is demonstrated that the simulations agree perfectly with the analytically obtained distribution functions, and those are indeed Gaussian distributions. The derivations presented in this study can also be used to derive transport equations in other areas of physics such as the theory of energetic particles interacting with magnetohydrodynamic turbulence.
A. Shalchi (Wed,) studied this question.