Empirical model of magnetic field line spreading in isotropic turbulence with zero mean field

In many cases, the random walk of magnetic field line in isotropic turbulence with zero mean field is appropriated to describe the transport of energetic particles in the interstellar medium of our Galaxy. To understand the transport, our previous work determined the asymptotic field line diffusion coefficient by using Corrsin’s hypothesis and presumed models of field line spreading. Two of those models of field line spreading are the diffusive decorrelation (DD) model and the random ballistic decorrelation (RBD) model. The variances of the field line displacement in, say, the x direction for the DD and RBD models are assumed as σ x 2 = 2 D | Δ τ | = 2 ( λ ∼ / 3 ) b | Δ τ | and σ x 2 = ( 1 / 3 ) b 2 | Δ τ | 2 , respectively. τ is the field line displacement parameter defined as dτ = ds/B, where s is the arc length along the field line and B is the magnitude of the total magnetic field. D is the asymptotic diffusion coefficient, b is the rms magnetic fluctuation and λ ∼ is the ultrascale. Comparing with simulation results, the DD and RBD models predict the D values with ⩽ 15% error and ⩽ 21% error, respectively. To improve the theoretical model empirically, in this work, we assume that the proper model the variance is σ x 2 = β ( b | Δ τ | ) α , where β is a proportional constant and α is an exponent. We extrapolate β with the proportional constants of DD and RBD models. Comparing with the simulation result of Kolmogorov turbulence, we obtain α = 0.8694. To test validity of the model, we compare the theoretical results of σ x 2 = β ( b | Δ τ | ) 0.8694 (formulated from Kolmogorov turbulence) with simulation results of two other turbulences: IroshnikovKraichnan turbulence and weak turbulence. The theoretical results of the empirical model match the computer simulation results very well (with ⩽ 0.9% error).