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

Abstract

Abstract In many astrophysical phenomena, understanding the diffusion of the magnetic eld line random walk (FLRW) is central to understand cosmic ray transport. In 3D uctuations, the behavior of the FLRW can be characterized by the Kubo number R = (b/B 0)(l ⫽⃥ /l ∧ ) [1], where the parameters b and B 0 are the rms magnetic uctuation and the large-scale mean eld, respectively. The parameters l ∥ and l ∧ are coherence scales parallel and perpendicular to B 0, respectively. For isotropic turbulence, in which l ∥ = l ∧ , Sonsrettee et al. [2] found that Corrsin-based theories can be applied to study the FLRW’s behavior for a whole range of R by varying b/B 0. Sonsrettee et al. [2] used Corrsin-based theory with three models of eld line spreading to examine the R-scaling of the asymptotic diffusion coefficients for the FLRW. The models are the diffusive decorrelation (DD) model [3{5], the random ballistic decorrelation (RBD) model [6], and the ordinary differential equation (ODE) model [7]. To improve the theory of the FLRW in isotropic turbulence with B 0 = 0, Sonsrettee [8] proposed the empirical (EMP) model of magnetic eld line spreading to determine the asymptotic diffusion coefficients. Benchmarked against the previous models, the EMP model is the best model to predict computer simulation results (with ≤ 0:9% error). In this work, we extend the previous works [2, 8] by formulating the EMP model to explore the R scaling FLRW behavior in isotropic magnetic turbulence by varying B 0. In the limit of very low R, we obtain the the closed-form solution of the FLRW for the EMP model. In order to develop the closed-form solution at any R, we employ the Padé approximants to the EMP model. The EMP model predicts that, with increasing R, the FLRW behavior transits from quasilinear diffusion to Bohm diffusion. This work shows that the theoretical results of the EMP model match the computer simulation results for the FLRW in Kolmogorov turbulence better than the other models significantly.