Ratio of path length ⟨S⟩ of random-walking field lines to path length S₀ of the unperturbed field line, as a function of δb∕B₀. Here ⟨S1⟩ is based on the simple estimate in Sect. 3.1, while ⟨S2⟩ is based on the more rigorous formalism developed in Sect. 3.2; both of these cases are for transverse fluctuations. The pink and green shaded regions represent the cases of isotropic (Eq. (7)) and 5:4:1 (Eq. (9)) fluctuations, respectively. The lower and upper bounds of the shaded regions correspond to the cases of positive and negative δb_z, respectively (see Sect. 3.1).